Yes, the bullet and primed case with powder are loaded separately. Generally, the bullet, bore, throat, alloy, etc. are decently matched for the process, but it doesn't have to be.
If it were me, I'd consider trying what's called a plugged case, brass with a length of dowel in it. The idea would be to push the bullet into the rifling to whatever depth chosen when the plug is fully seated, maybe into the throat just ahead of the chamber.
The powder in the case does not need to be contained. If it were me, don't use any card or wadding. In a somewhat similar situation, I've use a layer of thin mylar tape over the case mouth, but a stopper in the case can be pulled off just before it's loaded in the rifle. If someone were inclined to, the muzzle could be tipped up to shift the powder back before the rifle is leveled off to fire.
I'd consider looking up, if I'm thinking of the right .360 2 1/4", breech seat loads for the 38-55, and maybe the 32-40 to get in the ball park. Who knows, maybe one of the 4227 powders would do the trick. There are other thoughts, but as mentioned earlier, if it were me, I'd look into options to get a classic rifle back out in the field.
Only guessing with the new info you provided, but to load a fixed cartridge in that chamber at 1.8 inches, chances are it would look like a bottle neck or at least heavily tapered. Anyway, best of luck with it.
