RE: Throw & Grow
Try this if you can. As soon as possible, mow the spots as close to the ground as your mower or a weed eater will handle. Spray the food plot area thoroughly with "Round - Up". Generic such as Eraser will work. Wait a couple of weeks. Go back in a "till' the area as best you can. Take a soil sample and sent it off to be tested for pH. Cost for the lab test is minimal.
Meanwhile, check with your local county ag extension agent or state's ag university for info on what to plant. Clovers, rapes, winter peas etc. are all area specific to some degree. I would not advise you to spend the premium $$$ for commercial "buck clover mixes". I went this route years ago with White Tail Institute's "Alpha Rack" and "Imperial" clover... and tried their no-till product as well. Followed the instructions to the T. I could not even locate a sprig of the "Alpha Rack". The Imperial came up fine, but about 50% or more petered out before the season got rolling. The no-till? What a joke. May as well have seeded with grits (oat meal or cream-of-wheat for you Yankees !!!)
Wasted good hard earned $$$ on a "product" that faired poorly at best and that was later substituted for with a mix of good, local growing stuff for about 30% the cash out lay.
You indicated you have small areas you want to work. I would think that pH correction would be at least affordable using pelletized lime .... and it sounds like you could manage this with what you have at your disposal. It is expensive no dowbt when compared to spreading ag lime, but I think from what you posted, this is a good option. Good Luck !