The little .45 Auto Rims can be loaded like regular SAAMI-spec'd .45 Colts - and then fed via an HKS #25 speedloader in your 22. Some folks go hotter, as the cylinder/frame/barrel on a 22, 25, & 625 (.45 ACP) was designed for 22 kpsi, not the old .45 Colt's 14 kpsi. A 255gr LSWC or the 250gr Gold Dots (Speer #4484) nearing 900 fps from my 4" 625JM are 'enough' for me. Some get them up to 1 kfps... not me. Of course, they can be loaded in the .45 ACP cases, too - then be moonclipped. I started using the .45 AR's for non-FMJ loads years ago - when I still had a bottom feeder - actually, a Marlin Camp .45 (Now gone.) and all ammo had to 'feed' properly in it.
I agree re the 8x .357M moonclips being more tedious to load into a 627 - that 625, or the OP's 22, & 'clipped .45 ACP ball ammo will spoil you. I did just get 50 more 627 8x moonclips ($50 shipped from Ranch Products) for my 627's. They load the Remingtons and Starline .357M's quite easily by hand - and many .38's, too.
I have had a few .44's over the years - I just can't imagine having their cylinders dished for moonclips. Just the vestige of the original cylinder's length, left in an outer ring to properly headspace regular ammo, would leave some unsupported case - and high pressure .44M's and that don't seem appropriate to me. It's the same reason I never dished my .454 SRH's cylinder to add .45 ACP's to it's diet. I feel okay with my .357M's - I never load them very warm at all. In fact, I don't believe I have ever made a round which would top 1,000 fps, anyway.
I'd stick with 'available' mooncips, too. My .44's are fine with an HKS #CA44 for the 296/696 & a #29 with .44 Russians/Specials/Magnums.
Stainz