The space has a lot of very compact clay, rock and gravel- very little actual soil. Are there any flowering perennials that will enjoy these conditions?

Have you thought about raised beds?

There may be some plants that will survive there, but I doubt there is much that will actually "thrive." Are there any weeds or wildflowers that grow there now?

Kateri said: The space has a lot of very compact clay, rock and gravel- very little actual soil. Are there any flowering perennials that will enjoy these conditions?

There are...
I'd need to think about it, and I'm running late... I'll come back later...

Agree with looking at what's already on-site or growing near-by.
Sounds like you may be in the mtns... And... A walk along a near-by mtn trail would amaze you with all the Spring blooming native plants!

Edelweiss?? They like hostile growing conditions.

Rock rose? I forget the genus.
Can you show pictures or the area?
Sun, shade?

I second @Lucy68, build planters that compliment the natural terrain and using the local stone. You can add planters to the mix. That will let you grow most anything you want.

You didn't tell us whether sun or shade... essential information!

I'm thinking maybe moss verbena.
Or woods ferns...

If you had seeds, Id give columbine a try...