FWIW (which is probably pretty minimal ;>), there was a company years ago that converted M1 carbines to .45 Win Mag, using standard carbine mags. I remember playing around with .45 Colt ammo at the time, and it looked like it would also stack nicely in M1 carbine mags. If you've got a carbine mag available, you might check to see (1) if a carbine mag is short enough, front to rear, to possibly fit in the Ruger mag well with some kind of adapter, and (2) how many .44 mag rounds (if any) might fit in a carbine mag with any possibility of reliable feeding. The .44 rounds would tilt more than the .45 Colt cartridges I was working with, so it might not pan out, but who knows?
Another (probably better) option might be to check the possibility of adapting a .44 Desert Eagle mag to fit, using a purpose built adapter. The factory mags are a lot more expensive than M1 carbine mags, but there may be cheaper aftermarket mags to experiment with. I built a 9mm AR mag well adapter using surplus Uzi parts, so sometimes the "do it yourself" approach actually works out quite well!
As always, IMHO, FWIW, YMMV, etc., etc.