Let's see, size regular in June in Arkansas, with no trifoliate. That is a pretty tall order. LOSP is actually a PI garden of sorts, and it is very healthy there with some beds of around a half acre or so.
Flannelman is right, there are several great caches in the park itself, as Susan and the gang are very geocaching friendly. As far as the PI, I would suggest taking along a long sleeve shirt and some gloves that could be slipped on when you go in for the find. I do this pretty regularly with very good success. I am dreadfully allergic to all trifoliate, and hopelessly addicted to geocaching, so that is how I compromise. The trick is that you need to be very vigilant when putting on or taking off the extra clothes, so that you don't let contaminated clothing come into contact with your skin. The other thing I do is to use a PI extract that I get from my local health food store. I have had excellent success with this, mostly as a preventative, but also to a lesser extent as an after contact remedy. Good luck and happy caching!
Guess what?! I got a fever, and the only prescription...is more cowbell!!