Tightening the 2>3 overlap in a 727

To answer your original post, NO, there is no "easy adjustment" to cure this. RPM flash between 2-3 is a fairly common Torquefliteism. The TF-2 kit addresses this. You would have as much work into it as installing the kit anyhow. So just save up and do the TF-2.

Backing off the band will make this worse. The band is releasing 2nd gear before the front drum clutches apply. If anything, you may want to tighten the band, but I would adjust it by the book first before I started monkeying with it.