Railrunner85:
Your Model 29-3 .44 Magnum was manufactured in late 1987 or early 1988. By that date it should actually be a Model 29-3E with the endurance package design changes, but S&W never let parts go to waste, so its highly likely that it shipped in 1988 after the -3E changes were announced. The barrel length should be 6 inches, the 6.5 inch barrel was dropped in 1979.
Barr:
Your gun doesn't match the performance center listings in the Standard Catalog of S&W. The 625-8 .45 ACP was introduced with the internal lock in 2001. Under the normal production it does list a 4 inch Jerry Miculek Special in June 2006, matt finish, rubber grips / combat stocks, full lug barrel, patridge front sight, adjustable rear, Product Code 160936JM. I'm guessing this is your gun.