Nice find.
The original run were called Mountain Revolvers and came with Pachmayr grips, that was the 629-2. Nice gun and it does kick a bit with those original grips. I prefer the Herrett answer for my revolvers. It helps to tame the recoil.
Another good choice is the X frame Hogue grip. I have one that I use on various guns.

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Lynnie, Professional Pest

The X frame grips I saw were on a very early 500 and had a red stripe down the back. When I fired this gun it hurt...like in about three rounds I was done. I understand that the newer ones are all black and have some extra cushion where they meet the middle of your hand. I never load anythiing hot anyways but was thinking of trying a set of the Xframe Hogues for this new mountain gun. They look a little bigger or longer so might not carry as well but the trade off might be worth it?? Alot of shooters dont like the Hogues or any rubber grip for that matter but for a gun I am going to shoot they look and feel just fine to me.