There are many species of clover, and they can prefer many soil types. There are two perennial types commonly grown. According to Wikipedia, Red clover (Trifolium pratense) grows from 8-31 inches tall, so it's not a lawn substitute. It has a deep tap root that makes it more tolerant of drought. It improves soil by fixing nitrogen and adding organic material as a green manure. White clover (T. repens) is low growing, forming mats as it roots along nodes of the stems. It tolerates mowing and prefers clay soil. There may be other better clover species and varieties that your local county extension agent can suggests. You should be able to find yours HERE.

Late summer is after the heat breaks for YOU in your area. If you live on Hudson's Bay, you could probably do it now. If you live south of Detroit, you should wait until the end of August. Usually the reason for seeding in late summer is that there is ample time before the first frost causes dormancy. It also gives you time to evaluate the coverage and add more seed in a few weeks if necessary. Clover should not need to be reseeded, because it reseeds prolifically. As for covering with 1/4-inch of topsoil, instead use 1/4-inch of compost. Adding topsoil when you have good drainage already is going to mess up your drainage possibly resulting in water in the basement. Note that as clover reseeds itself (prolifically) it does not cover itself with 1/4-inch of anything, and it grows just fine.

I am guessing that the 'clover' is Oxalis. A picture would identify it. As long as the area is isolated from other beds and you never transfer any plants or soil from that bed to others, personally I'd leave the Oxalis alone. You'd be fighting a never ending battle to eradicate it and it will not bother the Trachelospermum.

Hmm, Desmodium paniculatum (Panicled Tickclover) does look like a good match, thanks!!