For what it's worth, I have a small planting that's mostly salvia underneath a spruce tree.
They get full/dappled shade *all day* and while they're smaller than their full sun partners, they still do quite well.
I think they were harder to get established at first, comparatively, just because they didn't grow as quickly as the others.

Cargobean,

I have been gardening in the shade for 15 years, and I've found that many sun loving flowers do OK in part shade, but they don't bloom as much. My May Night Salvia do well with very little sun. I'm having success with Moon Beam Coreopsis in part shade, as long as they have good circulation. Mildew can be a problem with coreopsis if they they're too crowded, so I have mine on the front edge of a garden, where they can catch a breeze.

Astilbe is a good choice for shade, unless you're tree is a Maple. Astilbes and Maples do not get along well at all. If your tree happens to be a Black Walnut, you should be aware that there is a long list of plants that don't do well under Black Walnuts.

Another little known shade plant is Corydalis Lutea. These guys have pretty foliage, dainty yellow flowers, and they bloom from early spring - frost. The only down side is that they spread, but I don't mind because they have almost no root system, so they're easy to pull if they're crowding other plants. They're also easy to transplant.

Good luck!

I garden in shade to part shade in the hot piedmont of North Carolina. For me, tall phlox, salvia coccinea and s. farinacea do well (but the s. greggii not at all). Also, coneflowers, black-eyed susans, spigelia, daylily, iris, asiatic lily, bee balm, and spirea. These plants do receive middle of the day sun but only for about 3-4 hours total. I would not put astilbe in your situation unless you live in a cooler part of the country such as the Pacific Northwest. There is a new foxglove hybrid called Digiplexus Illumination Flame that might be worth checking out. It's more sun tolerant, has repeat bloom periods, and is supposed to be a true perennials (vs. biennial). I don't know much more about it since it just came out this year.

As for the coreopsis, I don't know the answer to that. I've only tried 'Baby Sun' and it died on me but I think it had inadequate drainage and rotted. There are a lot of intriguing new coreopsis varieties coming out and it will be interesting to see if many of them are part sun tolerant.

3 to 7 is pretty shadey. I think the worst thing for plants is to be shaded all morning and the be blasted with hot afternoon sun. Morning sun is what everyone wants. Even if you have afternoon shade say from 2/3 on, things will do beautifully. There are so many plants that will like your situation better but some do okay. There are some salvias that like/prefer some shade, but do not think coreopsis.

Perennials are pretty easy to move. Try it for two years, see how they do. 2, because the first year after transplant they may be slow. Shade varies. If your shade is bright, that may be enough for the plants. After 6, the light is probably too mellow.