Well right now you have a Type II '61. Same as I did to my .38 Type II when switched to Navy gripframe. Of course, Colt only ever made one sample of that. I would be afraid that if you tried to reshape the barrel into a '61 R-M shape you will have problems with the ejector mounting.
Always wondered why Uberti never made the '61 R-M. They already have everything else, just need to make a new barrel.