You MKI owners can correct me but if I remember, there was a mod to add a cooler for the stator on the early bikes. While you have the cover off you will want to check to be sure you have that mod installed. Those that have that year can be more specific as to what to look for.
What all readings did you get to determine that the stator was bad?
Here is the full test for the charging system.
http://www.venturerider.org/forum/showthread.php?t=81297
I think you missed the point on the trans swap. Even though your parts bike has a good 2nd gear. It will still fail even after you go through all the work to swap it it out. I realize that it is good now, but it will fail and you will be doing the trans swap all over again along with all of the time and expense of another gasket set. If you are going to do a trans swap you would be best off getting a trans from an 86 or newer to swap in there. The weak part was fixed in all of the 86 and newer. You can get a trans from all the way up to a 2013 and it will drop in.