If you can find ammo, I think a rifle similar in form factor to your big game rifle in .223 is a better practice tool than the often much smaller and lighter zero recoil .22LR, but any practice off the bench is good practice.
One little drill I did with my son was to put 3 - 18" paper targets each at 100y, 200y and 300y (total of 9 targets). Then had my son take 5 shots at each distance from 3 positions - prone over a pack, from a knee off of sticks and standing offhand. After his 45 shots we collected the targets and measured the spread of the 5 shots on each. In any where all were within a 6" circumference around the bullseye we called that a "GO". Throughout the summer he would repeat the process but for only the distances - one further than the previous GO. For example he was a GO at 300 prone over a bag so when we were at a range with 400y option he did that, otherwise, he skipped that one. But he was a GO at 200y for kneeling with sticks so he would practice just 300y kneeling next time. That meant he only needed 15-30 rounds each time depending on if he did 5 each or 10 each. As the seaon neared we repeated the first full exercise on a day with a bit of a crosswind. His "GO" from that day set his max shot for the upcoming trip for various distances. He got out to 450 prone with bipods and that is how he took his first antelope buck at 415y. But he would have passed on that shot if he had to shoot from standing as his go for standing was more in the 150y range if I recall.
