tomos_1: that flame cutting you see in the topstrap of that 629 is basically just 'flame etching'. I have never seen an S&W that had been so used or abused that the etching had resulted in any permanent damage.
The flame cutting or etching of the topstrap is caused by fast burning powders of the type that are used under lightweight bullets. This flame etching concern first became noticeable with the Model 19 357s and the use of high speed, lightweight bullets where the faster burning powders used would 'etch' the topstrap. However, this never created a functional problem with the S&Ws. There were some other revolvers that had some real concerns, but not the S&Ws in the magnum calibers.
I don't think your gunsmith friend has done you any favors. If that revolver is in such risky shape that he would advocate for the use of low powered loads it should be returned to S&W for repair or it should be de-commissioned and a new firearm issued to you. If the only problem you have, or see is the flame etching, you can follow S.B.'s advice and send it back to S&W for an evaluation and repair. Otherwise, I would shoot that thing to your heart's content and not worry about it. I have never seen a 'top strap etched' S&W go into functional failure and would not advocate the use of low powered loads - if not done right, they can create a lot of problems with pressure variances you don't expect.
As for hunting coyotes with that revolver - you can use any factory ammo you want to shoot, although the heavier loads would really be overkill. For Yotes, you can use any of the factory 180 grain loads or even some of the 200 grain loads - fairly easy to shoot and easy on both you and the revolver. HTH. Mikey.