If it were me, I'd clear out the rest of the tree that are still in the plot and hinge cut some trees surrounding the plot to let more sunlight in. If you are going to do a soil test, they will give you a recommendation on lime and fertilizer for what you want to plant. These should be worked into the soil. You know ...... tilled. Once you have removed all of the roots and things that tangle in the tines you should be good from then on. It's a pain but that's how your plot will do the best. I found this out myself as I have 1/2 dozen woods plots also. I don't think there is a miracle "throw and grow" mix out there that will give the results you're after without proper soil and sunlight prep. Good luck
Lime needs to be particle to particle contact with your soil. Now without tilling it can be done with a stone rake and man power. It will only mix the top few inches but will give you enough to get seeds started. Lime takes time, again it takes time to work. No I personally would not invest the money into bagged designer seed. Go to a farm feed /seed store or some place like seed ranch or Hancock seed. Or places similar out your way to buy the small amount you'll need. Read read read about the seeds. Look for lower light requirements, browse pressure, weed suppression. What plants will naturally draw up nutrients that may be used next year. A really small plot can get hit very hard in an area with high deer numbers . Also if you have chucks and rabbits. We actually have both those live in our timber not field edges. So many different clovers, fetches, brassica, greens. Things like small Burnett,sainfoin. Winter grains do not need to be just WW, oats, WR. Also timing as far as what to plant earlier to give them time to realize there is food there then what to over seed to produce food draws for later season. Then if you want plain ole deer candy . You can check out my in the woods low light cow pea planting from last year. Worked for me but you need to decide if it would for you Shop for best prices for such things.also I see you seem to be on a hill...consider water...those trees will not only keep water and any night moisture from getting to the ground but man those roots will suck the soil dry at their root level. and leaf drop will smoother shorter plants. Just things to consider as you improve the soil tilth and nutrients. All that said making them feel safe going in to check it out and not letting them be able to see it hundreds of yards away is also important. Why would a buck come in to check it out for doe if he can stand far away and see there are none.