You have a thread chasing dial so you CAN open the half nut just as long as you re engage it on the same spot on the same rotation on the dial as you reverse direction.
I hear you on the die, but here's a tip on how you can thread full depth up to the shoulder with a die... after your first run to the shoulder, reverse the die and cut with the back end, this will give you a full depth thread all the way to the shoulder (takes just a few extra seconds). Ciao, Marco.
There are many change gears - in part 1, I show every change gear with its tooth count. Without the knowledge of the transmission between the change gears and lead screw, plus information about the lead screw itself, I doubt any information I could provide would be useful.