Well, I don't know what to tell you. Both videos show doing essentially the same thing, just with different tooth count gears. If you have just the basic QC lathe and no extra gears, the second version is the most economical, requiring only a new 24 tooth gear. However, the second guy did fail to mention one other part that you will have to have. This is what the threading charts call a Steel Spacer. It replaces the 48T that was removed from the front right position where it and the one in the back right position drove the long gear in the gearbox. I am trying to determine the part number of that spacer. In place of the 40T sliding gear, you put first the 24T in the back position and then the relocated 48T in front.
The tumbler gear (stud gear on a 10" change gear lathe) is a 32T/16T compound gear. The 32T part is driven by either the forward or reverse gear on the tumbler. The 16T part drives the relocated 48T gear. That is your first (normal) 2:1 reduction. The relocated 48T drives the new 24T through the 9-70A bushing that they are both mounted on. The new 24T drives the remaining original 48T in the Back position.(its original position). That is your second 2:1 reduction. Finally, the original rear 48T drives the gearbox as it always has. That looks like it worked. I am going to order a 24T gear this afternoon, and if we can determine the part number, a spacer. When they arrive, I'll try it.
I'll add that the slowest cross feed rate has always seemed to me to be too fast for power feeding for milling. This will help that as well.