There are two ways I approach jobs like this. One I can do it with the barrel on the rifle or set up in the lathe.
Barrel on; Make a rod guide for the action. This entails drilling and reaming a 3/8 hole through a rod. after drilling and reamer turn the outside diameter to fit the action. Next take a piece of 3/8" drill rod and make a t-handle long enough to reach through the rod to the chamber. Do what ever is needed to hold the throating reamer on the end. Now you have a way of holding the reamer, guiding it and turning it at the same time. How to control the depth? Take a short piece of round stock the same size or smaller than the rod guide, drill and ream a 3/8" hole through it. Add a set screw from the side, slide it on the the T-hande before inserting the reamer into the action. Push the rod guide forward until it touches the rear of the barrel, run your reamer in until you just feel it begin to cut, slide the stop you have on the rear of the T-hande up until the gap between it and the rod equal the amount you want to lengthen the throat. Lock it down then crank away until the stop hits the rod guide.
barrel off and indicated in the lathe: Hold the throating reamer with a very short handle on it. Run it in until you feel it start to cut. I zero my travel indicator, start up lathe and cut to my number.
It's easy to over shoot your stopping point.
Dave