What about something totally different, what about using a plant that is red/purple in leaf and forget about flower matching/contrasting? Something like wiegela wine & roses or sambucus black lace or perennials like heuchera, lysmachia or sedum.
Another thought is to use the yellow in the flower color and find a variegated plant that complements it, something like calmagrotis eldorado or Hakonechloa macra 'All Gold'.

Flora

White would look pretty and fresh - very light tones. Maroon is quite pretty too (Smokebush) and would contrast well.
Love the idea of the foliage!!!!!

I think you'd have to match the intensity of the colour with something - so something that was REALLY blue or white or magenta or hot pink. Anything pastelly wouldn't complement it as well....

Check out some of the blue delphiniums. Some of the royal blues are gorgeous.

instead of complimentary colors - (yellow and purple), try a triad combination. Select the colors from either side of the complimentary color on the color-wheel. For intense yellow that would be a magenta and a blue-violet.

Another thing to consider is instead of an even distribution of complimentary color (like those checkerboards you remember not-so-fondly). Masses of yellow with only an occasional intense purple, would have a very different feel, and would really pop the color.

Purple and yellow are a favorite combo of mine, but I like lots and lots of purple with only an occasional spot of yellow to set it off.

Those are some great ideas! You've all got me nudged in the right direction.

flora2b, I have always very much disliked bronze foliage. Couldn't stand it, actually. But, now that you mention it in front of Ruds...I GET IT!! That would look great. I'm going to move my SEdum 'Autumn Joy', which I never really like AT ALL, to the Ruds. It's not foliage, but it has that same great bronze bloom in the fall. The foliage idea is something that had never entered my mind. I'm going to research those plants you suggested. Foliage plants are one thing I have learned nothing about...all in good time. Clearly I need to expand my knowledge.

I do need to find out about more white delicate blooms. I do have a Gypsophila pacifica, which is much more uncommon than the typical Gypsophila paniculata, and is a great filler. I almost ripped the whole thing out because when I inherited this highly neglected garden it looked gangly on its own, but at the last minute I decided to plop it in the Echinacea for filler. I should try to get some more of those seeds for filler in the Ruds. I believe that would be a "repeating element"? ;-).

Will check out the delphs, sprout_wi, haven't heard of the Royal series.

on_greenthumb and mandolls, I had TOTALLY forgotten until you guys posted that a couple of years ago I had seen pictures of hot yellow with strong magenta and had LOVED IT. Woo hoo! I don't have any strong magenta fall blooms now, but this week I'm going to pick up some Phlox paniculata 'Nicki' (in a 3" pot, so it's much cheaper). Had just seen that phlox and thought to myself, "Gee, I don't want that strong color." HA!

So, current plans are to move my Sedum to the Ruds, learn more about foliage plants, continue with the Delph Blue Mirror idea, and pick up some magenta. I think I have a plan! Oh, and I just remembered I have Joe Pye Weed that doesn't have a home. That would give a bronze bloom, too, wouldn't it?

(Looks like I've gone from having nothing for the yellows to having too much!)

Here I go again ..... putting in plug for GREEN. Something with different shaped foliage and or habit. Both your plants are blobby with small leaves. So how about looking for something taller, spikier, larger-leaved? Maybe something that blooms earlier in the year before the yellow is there and then provides a green foil later. You need to plan in time as well as space.

Deanna, sounds like an LSU fan's pansies. Any chance you were in Louisiana? I like to plant a mix of pansy colors.

I use a lot of bright yellows in my gardens and those I design for others, because a lot of native plants are very bright yellow. I tend to design in layers of them. Bottom layer could be a low ground cover sedum, then a layer of rudbeckias, a layer of bright yellow coreopsis and a top layer of maximillian sunflowers. Then I work on the "in between".
I very much agree with Floras ideas of using contrasting shapes (leaves and flowers) to obtain interest. All the yellow flowers I listed are sort of daisy shapes, so you'd look for things that are not daisy shapes, and leaves that are variegated with gold but not white (trust me on this one, the white looks better with a buttery yellow) - You'd be looking for things to tuck in, in between each "layer" of yellow. I am using Bluestone Perennials as my look up resource (because it is easy, and many of those plants are fairly easily available all sorts of places). With the very low growing sedums as the lowest level, ajuga would be gorgeous, or perhaps a groundcover veronica. The next level, I'd take that blue, but add another color: say take a blue speedwell veronica for the spikey effect, but throw in the Red Velvet yarrow which is a pinky red (so it will go with burgundies too) - these bloom early and would look super with upright sedums such as Autumn Joy. Amsonia is anaother good "middle size" plant and it has a sort of thin, ferny leaf and blue flowers earlier on. Why is it so great? The actual shape of the entire plant is much like a grass and it turns a stunning gold in the fall which will compliment the brown seed heads of the golden flowers just before winter sets on you.
Aquilegias can also fit into this area and can be tucked in so many places as they really take up very little room. Think about more of the blues, and there are some reddish ones too such as Bartow Red, clementine red, Ruby Port.... that are on that blue/pinky/red side that will fit in nicely with the gold. So you dislike the burgundy foliage, which is fair enough - that color is coming in with flowers...how about grey foliage? Artimesia can work well, or perhaps you'd just prefer to stick with a dark green, and then some dark green and gold. As for dark green there is Ladies Mantle. The flowers would also compliment the scheme and the huge lovely leaves would be perfect. For a slighty different shape of leaf consider some bearded iris: Safari Sunset would be stunning there.The next level is slightly taller, and native Baptistas will fill that bill so nicely! Gorgeous plants, great dusky bluish green foliage. So you dislike the burgundy foliage, which is fair enough - that color is coming in with flowers...how about grey foliage? Artimesia can work well, or perhaps you'd just prefer to stick with a dark green, and then some dark green and gold. As for dark green there is Ladies Mantle. The flowers would also compliment the scheme and the huge lovely leaves would be perfect. Orange (with burgundy spots) tiger lilies, daylilies and Blackberry lilies could also fill this spot and add a new punch of color. These particular oranges do go well with the burgundy flowers.
Next up you'd want some flowers and foliage with even more height. Think about perhaps some nice burgundy flowered hollyhocks, Shenandoah panic grass, or a burning bush which would be that dark green in summer and a fantastic glowing red in the fall (not really burgundy, but blazing red!), Brigela Wigelia has great variegated foliage (with gold and green) and a deep reddish blossom. Want to bring that blue back into the "toppermost" poppermost level? How about setting a nice blue clematis to clamber over some green shrubs?
It will be a very bright garden, no doubt about it, but it can work really well. This is often a color scheme I use against a dark sort of burgundyish reddish brick home or dark grey painted homes. It would work well for other backdrops too, and if you do not have a back drop set, I suggest against taller green shrubs to set it all against.

I love magenta and orange with bright yellow/gold. Reminds me of birthday parties for some reason.

I also love a mix of yellows, oranges, and whites, which is really fresh and spring-like. Those are the main colors in my garden. There are TONS of good roses in these colors. Chartreuse is a great addition to these combos: Golden Feverfew, Lady's Mantle, etc.

Blue, yellow, and white are pretty together too, but blue flowers are harder to come by. I like blue irises, delphiniums, and sea holly.

Another great bright yellow plant is yarrow 'Moonshine'. Or is it 'Moonglow'? Anyway, the yellow one with the gray foliage puts on a show.

Like you, Deanna, I dislike yellow and purple. I also dislike orange and blue or purple. But I love blue and purple, and I love yellow and orange. A dilemma! And then there's my love of scarlet red...

Renee

Will continue to look for the greens, flora_uk!

natal, I'm sure I've been to Louisiana during pansy overdrive, but there are enough high schools with purple/gold colors (my college had those colors) and uninteresting professional landscapers to give me an LSU headache! I'm sure Auburn is full of orange and blue pansies, and I'll bet a Roll Tide fan somewhere is frantically working on red pansies.

GGG, that's a TON of helpful info! Will spend quite some time investigating your and flora's suggestions.

Renee, having seen pictures of your amazing gardens I feel quite glad that you dislike yellow and purple--gives me a little confidence! As for scarlet red, I have Maltese Cross planted beside the Ruds now because last year I thought I'd love red and yellow. But, after putting red and yellow in planters i decided it just didn't give me either excitement or calmness. I do love the red of the Maltese Cross, though, so I'm certainly not getting rid of them. I know that wisely planting per the suggestions here will bring out both the Maltese Cross and the Ruds and avoid having red/yellow as center stage. Red is my favorite color!