SKS is the only rifle I can think of in your price range. I have killed both of my hogs with the 762X39 Wolf 154gr soft points. Neither of them took a step after being hit. Mine were taken in fairly thick brushy areas where 75 yards would be a long shot. As far as recoil goes, the 154gr Wolf kicks less than the standard 123 grain loads. Velocity is around 2200 fps. Both of my shots were pass through with a tennis ball size exit. Even if your budget was higher, I think the SKS may serve you well for swampy brushy areas.
Make a hole