Crimson clover is one of the more depth tolerant clovers out there. Think it can handle up to 1/2". Medium red is 1/4" maybe a bit more. Most other perennials are 1/8 to 1/4". Do you have a separate seed box, or just using an older grain drill? Sometimes offsetting the small seed tubes more to the side of the coulters helps keep the seed higher up in the dirt.
Corner of hay field, keep it a hayfield. You could spray that 1 quart / acre gly or clethodim to kill the grass. cleth stuns clover very lightly, usually because the surfactant you need for it upsets the clover.
Put oats, wheat, or winter rye in there after you spray. If the weather is still dry, focus on the rye. And put some clover in there too. Mow the area short, cultipack or roll with tires. In in NY, we do this at or a bit before labor day. Down in NC, maybe spray labor day and put the seed in and then mow a week or two later. Gly you can plant pretty much when you spray. clethodim has residual effects, especially on its target grass. You definitely should wait 2 weeks. Cleth is handy to have, can spray around fruit trees or bushes and it doesn't bother them. commonly used in tree farms. The smell brings back memories of grape vineyards my family owned.
Just a broadcast of rye and clover with a low mowing should make things more attractive to deer.
It is very common practice to mix cereal grains and potash together and broadcast. 10 bags of pelletized lime mixed with the seed would be about 1/2 ton / acre equivalent. If concerned about the potassium pick up 2 bags of potash, or 2 bags of 6-24-24 would work good too. Oats need the potassium more than the other 2 do.