How about Bee Balm aka Monarda?. One of the cultivars 'Cambridge Scarlet' has 4-5' stems and has large scarlet red flowers all summer, or 'Colrain Red' grows 36" high and the red bloom has a touch of yellow. These are tall perennials so may be higher than the Rudbeckias and be able to grab some of that sun. If not the afternoon sun may be enough for it to thrive. Good Luck!

It may be true that the rock keeps the roots of some sun plants too cool, but you might have better luck with sun plants if you put the plants in when already at a mature size before the rudbeckias come up in the year. You don't say if you're trying to start from seed back there, which would be hopeless because it's cool on the ground.

As for selection, I'm wondering about a red astilbe, but I have to admit I don't like the mental image of that with the rudbeckia. You could go with coloured foliage - Eupatorium, or Joe Pye weed, in one of the "Chocolate" varieties. How about a tall red rose otherwise?

Maybe Cardinal flower, Lobelia cardinalis? It's definitely red, and seems fairly flexible about sun and shade.

my tiger lillies do pretty well in shade/part shade. they are nearly 5 feet tall. maybe they don't have a long enough bloom time for you.

Try some astible or foxglove. Both are shade flowering plants and both are tall. Astible grows to about 3 or 4 feet I think and comes in an array of colors.

Be sure you have enough moisture if you choose to use astilbe. Astilbe are moisture loving plants. The foliage will dry up and the plants will go dormant if they do not receive enough moisture.

Any lily would love to be there, cool roots and warm head is all that they need. Most of them, except pixies will be taller than rudbeckia and you could chose different bloom time from late June till mid-late August, prefered color and height among many Asiatics, OT or Orientals.
Just noticed, you are from MA, so you might have a problem with lily beatles, but beside that, from cultural point of view lily should work perfectly.