The .44 Carbine is not in any way, shape, or form built on a 10/22 receiver. They're completely different rifles except for the fact that they look (and feel) alike. The .44 came before the 10/22 - I read somewhere that the 10/22 was originally intended as an inexpensive practice rifle for owners of the .44.
The .44 Carbine stock is retained in a manner very similar to the M1 Carbine's stock. In addition to the barrel band there's an attachment point at the back of the receiver.
I took my carbine apart to clean it when I bought it, figuring it'd be a piece of cake since I've had my 10/22 apart dozens of times. Wrong! What a hassle. It operates in a completely different manner than the 10/22 and sure doesn't look like it was designed to be disassembled easily like, say, a Garand. So, 10/22 triggers are definitely out.
I think the tubular magazine is limited in length - and hence capacity - by the gas piston assembly being ahead of it inside the forearm.