I am the last person to suggest one needs a reason to buy another gun but why stop at the .22 magnum? The .22 Hornet gives even more oomph and opens the door to using many really good bullets vs whatever .22 Mag you can find near you.
I think one reason I have never warmed up to my .22 magnums, is a lack of choices and none have ever been as accurate as some of the .22LR’s I could also choose from.
No need to gamble on what is more accurate, test both and you will know.
My issue with a "real" center fire rifle is I just did not want that much power. I see in this application little difference between 22 hornet, as well as being even more expensive over the 22mag, as not bring all that much more to the table over the 22 mag.
If going in cold, like I think the OP is doing and buying new LR is cheaper over mag, and mag is cheaper over hornet, you don't really get more mass but a bit more zip for more cost.....basically the same argument as LR has over mag, you get more zip but not much more mass.
You would not have to worry about it leaving the animal even with a pretty iffy shot. The reason I liked the 357 was the extra mass of the bullet, it is a thumper. For the smaller you can step down to basic 38's or even hotter + rounds and still stay inside the raccoon.
My issue was about 200 yards away was stuff I really did not want to hit....so I did not want a "real" rifle again. I had originally wanted one of those old ruger 44mag rifles that look like an over grown 1022, just thought it would be fun. Never could find one I was willing to pay for. I found a camp 9 and did use that for a while, but....well I am a gun nut and I have a problem....still wanted that 357 lever, so got it and really liked it.
I did not bring up before but Ruger makes the 77 in 357, but it is just flat stupid expensive. It is a plastic stock and stainless deal, the price has pushed me away from it for years.....this year I am just going to order one, hell with it kind of thing I deserve a new toy.
I think the 357 if looking for something new is really pushing a great many buttons on the yes side, but then so does a 9.....wonder if anyone makes a 9 lever gun.....if they do please don't tell me.