727 not hitting second hard enough

Like rusty said I've installed these trans go three shift kits and it should be fully manual meaning you have to put it in first for it to be in first and take off if you put it in second or third and take off from a start it will start and second or third. You must shift all the way up and all the way down.. take all the kickdown linkage off and put a piece of baling wire through the eyelet of the kickdown lever on the transmission and pull it all the way to the back of the transmission till it can't move and tie it down...
it doesn't sound like this was put on a brand new transmission so always keep in mind that the transmission could have been wore out pretty well before this modification. If the clutches and seals weren't up to the task it could just be creating more problems...
Also there should have been a screw right there where the kick down which ( it's a pressure valve) is where there was something to turn in till it was flush with the outer housing is the general adjustment called for... If this other stuff doesn't work unfortunately you would have to drop the pan again and possibly adjust that in just a little bit more to create more pressure for the shift. Again with the used tranny that might just have even more catastrophic results...