I have a 727 behind a 340 that I installed a couple of years ago. It was fully rebuilt a few years before I bought it. It had never been used before I bought it. It was done by a quality shop for the purpose of drag racing and had a forward manual valve body installed. It worked great since I started using it, very positive shifts with zero overlap and it would always chip the tires on 1-2 shifts. Near the end of last season I took the car to the drgstrip and I noticed that the trans was shifting into 2nd by itself. I chalked it up to a loose linkage which was allowing the selector to jump into 2nd by itself. The problem is for the rest of the season I noticed the 1-2 shift was much softer and I would have to really jump on it to get any rubber from the 1-2 shift and it felt like there was some mild overlap between 1-2 before it would fully shift. My hope is that it just needs a band adjustment. Does this sound right or is there something else that could be the issue.

Sounds like time for a fluid and filter change along with the band adjustment.

A soft shift like you describe from a previously hard shifting trans. could indicate some loss of hydraulic pressure from leaking seals or rings. If you have a pressure gauge it could tell you a lot.

x 2 .. on a line pressure check. How is your fluid ?

A firm 1-2 shift relies on a properly adjusted kickdown band, check that first.

Yep.