Harth, if you are consistently hitting targets 3 inches in diameter at 300 yds with a 22lr, you probably need to be sharing your secrets rather than asking for advice.
I see you included deer as one of the species you intend to hunt. Although many deer have been taken with a 22lr it is probably illegal in your location and certainly not advisable. In my neck of the woods, hillbillies including myself, killed deer with 22lrs because they and their families needed meat for the table. This was usually done at very close range and only when precise shot placement was possible. Most folks had an old flea-bit hound to help clean up the mess if things didn't go well.
If you are hungry and don't have anything else to use, I reakon one has do do what he has to do. If you are starving and you must, keep it under 25 yds, broadside standing shots only, put it low 3 to 4 inches above and slightly to the right of the elbow, give it an hour or so before attempting to recover it.
Really, shooting the 22lr at the distances you prescribe is for recreational purposes only. Frankly, reading your posts makes my hair stand on end.