One proven method is get a similar 22 and just shoot. 5000 rounds a year is nothing and costs about nothing.

Another is the mentioned dry firing. But one way to train the mind and eye and finger(don't laugh this really works no matter how stupid it sounds) is to get the rifle to the range on sand bags. Pull the trigger as soon as you are on target. Do it thousands of times. 10-20 minutes a day helps. You don't see the wobble because you are on bags basically. And you are training the eye to move the finger immediately as soon as its right. This is a super training tool for the offhand stages in matches I shoot. One reason offhand is hard is because you see all the movement. ITs hard to train around it. Best to basically make it a reflex that as it approaches the shot goes instantly. In offhand if you wait till you see it (the "perfect shot") and then try to do something you are way too late. Learning to either shoot it as it approaches or let your reflexes do it is best.

That being said if you were in the situation-- pin up pictures of deer around the yard or house and dry fire at them. With a centerfire you don't really need a snap cap either. Make them tiny too.

Practice live fire further than you would shoot. It makes the real shots seem easy. I practice my bow at 60 yards. The 20 yard shots are easy. I practice pistol at 50, shots closer are chip shots. I practice rifle out to 1000. 100 yards seems like a cake walk. So does 300 or 400.

Jeff