2 square miles is a big area. I hunt deer in a 1 square mile parcel of land, and they NEVER leave. It is unfenced, however, and they could if need be.
To each his own. If you feel the hunt is ethical, it's you that looks back from the mirror in the morning. Primitive bow vs Buff... sounds like even odds to me. It's not just gonna stand around.
Your bow? If it was me, I'd use something else. I have a 62" NTN, hickory backed osage, 70#@27", tillered bendy handle. I'd use heavy wood shafts, probably fir or ash, and a 2 blade broahead, probably a 190gn Grizzly. You want PENETRATION, not speed. At <20 yards, tragectory won't matter.
I think I'd take a clean pair of shorts, if you go without back-up!!