You can do that. On the surface, they're fine, just don't dig them in. They'll take a while to decay, so expect to have them around for a long time.

And by "LIGHTLY" i'm pretty much meaning that the edge of one chip does not touch the edge of the next chip if they're bigger chips. Things like slugs love to make homes under them in the dark and damp and...well, you don't want that to happen. Smaller chips can go much closer.

I have a horror story about 1.5" chips I could tell you, but I won't.

If they could be rendered to sawdust, that would certainly be better--but it's by no means necessary. Still, the smaller the chips, the better.

I could give you a better guide on density if I knew the chip size...

OP I suspected that. Last year I used the wood chips to create paths in the woods. (Much thicker than I was think about for the yard). After a year that paths have nearly disappeared..

Im finding out bermuda thrives on hills. I too live on a hill with red clay soil and been doing alot of yard work over the last 4 yrs. Taking down unwanted trees and spriging about 15,000 of bermuda to put my lawn at around 25,000 sq ft now. All 100 % bermuda with no weeds in front, side and back yards. Grass seed doesnt like red clay in the very hot summers like we have here so it will probably struggle for you too, untill you mend that red clay soil

Ive used mulch like you buy in bulk as a top dressing over the spriged areas. It seemed to make the bermuda to fill in faster. I did have some washout because we had some very hard rains here this past summer. Putting it thin means you will get some washout, especailly on a incline. If you mulched it like a bed(3 inches thick) it would absorb a hard rain and not have wash out but you wouldnt get nothing to grow because of how thick the mulch is