I recommend a S&W Shop Manual (about $45 on Ebay) and a beater model 10 from someplace like Centerfire Systems and a hollow ground screwdriver that fits the side plate screws.
Most problems are actually not that hard to fix, actual revolver smiths are getting to be hard to find.
First thing I always check with a timing issue is clean clean, then endshake, then the hand. Also if the gun doesn't carry up before releasing hammer, does it do with empty cases in chambers. If its empty the extractor might move enough that it fails to carry up, while it carries up while loaded. The first is not a true fault. Excess end shake allows the cylinder to move forward slightly and then the hand slips by the tooth a bit sooner. Easy fix. Over sized hands are available. Midway has them for about $19 for factory oversized up to $33 for Power customs