A wooded acre is going to draw alot of critters! Rabbits are prevalent even in non wooded city blocks. You could try a couple things: a non-neutered outside Tomcat (with claws), and subvelocity 22 rounds, like CCI CB caps if they still make them. (Not as noisy as an air rifle.) The Tom can be in the house daytime to sleep, but toss his butt out at night to work. Some dogs are better at running rabbits, too. I don't know if you get snow, but I used to pop rabbits at night just by ambient light in my scope no problem. Wa la! Supper.

My sympathy. I had to fence off my garden.