I don't see any problem with a 22lr. My first pig I took was with my Winchester 290 semi-auto. I had a frontal shot and put 6 rounds of Remington target round nose into its head at 35yds & one into its chest when it turned away from me after charging at about 10yds.
I heard it crash in the brush not far away. Since your in an area where only rimfire is allowed I'd just make sure your shots count or have the ability to throw a lot of bullets into its head. Now that I think about it, I should have only shot the piglets....would'a been easier to drag out & clean. At the WMA shack it had she weighed in at 130lbs. Not that large compared to the ones I've seen online....but still heavy enough to drag & load myself in the pickup bed.
After that hunt, I made a trade for a Savage 24 in 223/20ga for my small game season hunting. Pig season overlaps all other seasons here in GA., but you can only use the weapons allowed for the season thats open on WMA land.
Good luck on your hunt!