need transmission schooling

As mentioned the transmissions are the same for a 340 and 360. Just the converter is different. If you want to stay with a 727 the 71-73 is generally considered the best to start with but from what you describe I don't see why a properly built 904 wouldn't do the trick. Like Cannucky said you'll get more HP to the ground with a 904. Less rotating mass to absorb HP