Semf, let's talk accuracy a sec.
First, read this:
http://www.sixgunner.com/linebaugh/accuracy.htm
As you'll see, the really critical areas are the primary frame dimensions and holes...base pin alignment with the barrel mounting location, cylinder (just about everything matters), etc. If those are wrong, the gun's not gonna shoot and it's a royal pain to fix...in some cases, not even possible.
You're not going to be messing with any of that. If it's good now (and it sure sounds like it is) then it still will be.
The worst you could do is screw up the trigger pull a little but if you're careful you can even deal with that yourself and it's not that likely you'll have a problem. The New Model SA action is pretty simple in there. Absolute worst case, any number of gunsmiths can do a $75 trigger job.
Now, while you've got the innards all out, you might consider a $35 freewheel pawl addition, allowing the cylinder to spin both ways with the loading gate open. It's a Power Custom part.
Finally: there's a used-parts-market demand for the bits your gun is wearing now. Not huge, but it would surprise me if you couldn't get $75 for all the used bits coming off...maybe $100
. Or keep 'em all and the resale value of the gun goes up a bit.