I've got the exact opposite problem. Earlier this year, after reading a substantial amount of Elmer Keith, I went on a .44 mag kick. I picked up an 8 3/8th 629-4, a 4 inch straight 629 (pinned & recessed), and a 6 inch 629-1. The 629-4 mics at .4295, but the others mic at .4315 or .432.
I want to shoot cast bullets in my revolvers, so it's important to have tight chamber mouths. Ideally, from what I've read, a cast bullet should be .001 over the chamber mouth diameter, and then the chamber mouths should be at least equal to or .001 over the bore diameter. This 'step-down' effect means that the cast bullet is fully engaging the rifling at all times, and generally has an extremely positive effect on accuracy. If the bullet is smaller than the bore (or chamber mouth) diameter, either gas blowby occurs, or the bullet deforms obliquely. Each of these is detrimetal to accuracy.
S&W found that tight chamber mouths lead to greater accuracy, which is why for the 629-4 and later they tightened them up. They also beefed up the cylinder and crane to stand up better to hot loads.
I agree that .427 is way too tight, but your best bet would be to measure your bore diameter, and ream out to .001 or .0005 above that.
I would seriously trade my 629 and 629-1 straight across for comparable condition 629-4 or later, as long as it didn't have a lock. Each of these pistols is in good (95+% condition), but I'm not so much interested in the nostalgia as in shooting great. Don't get me wrong, they do shoot well, but I'm hoping to wring the utmost accuracy out of them. I'm somewhat of an accuracy nut.
-John