Not sure how big of an area you are going to do but if you find low pH back there, toss all your wood ashes back to help raise it up.. Much faster than lime but not as practical unless you have a lot of ashes.
If you need to raise the pH fast, some KOH (Potassium Hydroxide) will bring it up almost immediately.
The easiest way would just be to use round-up, then get a small rototiller back there and plant sweet corn... About a month after planting, throw down a light application of 12-12-12.. then again about a month after that.... As soon as you see the cobs forming, hit it heavy and hard with 46-0-0 (straight urea)...
That sweet corn will pull those deer in hard and it doesn't grow much taller than 4 feet or so.. The trick is to plant enough of it that they don't destroy it all during the growing season. They'll start eating the leaves even before its a foot tall.
Once you plant the corn, you can also plant rape seed around the corn to keep the weeds down and beans interlaced with the corn to add some more nitrogen into the ground.. (beans make their own nitrogen and the deer love them).