Very good thought.. I would check all the connections at the starter.. Being your stating that it didn't engage when hot. Is really learning me to be your stater contacts are warn out. I don't see how many miles on this starter listed. I had one 3rd gen that the connector in the back of they ignition went bad. This fooled me because it acted just like a starter problem. Hence, I replaced a starter for nothing as it was just a worn contact at around 220 to 230K miles. Alternators brushes wear out between 180 to 230K on average so if the starter is OEM with some mileage that maybe the issue. If the starter is aftermarket who knows how long they will last.

I hope this helps as I don't think it was anything to do with the transmission change.. I think you just developed a starter issue or a problem in that starting circuit is all. :-)