727 doesn't shift into second gear like it should

To be honest with you I forgot to look. The transmission is a '70 model. And it is still behind the 340 it came from the factory with. If that might help with a guess at the ratio. I had 2 1/2 turns stuck in my head and that is what I ended up doing. I could probably go back and tighten up the front band a 1/4 turn if the ratio calls for it but I don't think it would make a difference as far as the 1-2 shift. Next time I take the pan off I will be a little more aware of what I am doing and check the ratio to be sure I have the exact adjustment. But even going from the 1 turn out to the 2 1/2 turns out still made no difference.

1970 727's that came behind 340's generally had the 4.2 kd lever so your close on the adjustment. It should actually have been backed off 2-1/4 turns rather than 2-1/2 but if anything having it backed off more should have helped the situation if I'm understanding you right and it's shift overlap. There is one other thing that causes 1-2 shift overlap and it's the cushion spring inside the rear servo. When you manually shift it the rear servo basically has 2 springs that need to come off before it's fully released. With a shift kit installed 2nd gear hits so fast the rear servo doesn't have time to fully release before the front band is applied. There is a fairly simple mod to do to overcome it which involed removing the inner spring and shimming it solid. It's main function is to make the 1-2 shift softer to please the older generation that doesn't like a harsh shift so eliminating it for performance is not big deal. But here's the catch. All 1971 and earlier HP 727's I've been into had a spacer where that spring is so basically the mod was done from the factory. But who's to say the rear servo wasn't switched out with a standard servo sometime in it's 42 year life. The only way to know for sure is drop the pan and check so see if it has a spring or shim in the servo. You might want to ask your rebuilder if he did any mods (drilled anything, added any check balls he thought might have been missing, etc...) or swapped the rear servo while rebuilding it since you said the 1-2 shift was fine before.