I am almost 100% sure that your 629 is a round butt. Forum member 75vette will be along shortly to confirm.
Try the Pachmayr Diamond Pro grips. You can find them on the web for 20 bucks or less but they are the best I have found. They are very comfortable, absorb recoil well and fill the hand. You need the N frame size. I think they are better than the Houge X frame grips.

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Accuracy supercedes Speed