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You are correct about being careful not to change the lift angles. Fortunately you have the perfect machine for doing the job. Your Taig lathe will work beautifully for this. If you have a fine grinding wheel or a mandrel that you can glue emery paper onto that will fit in the spindle of your lathe you should be good to go. The idea is to rig up a small fixture that will allow you to do one of two things. You can remove one pallet at a time and clamp it onto your cross slide vise or tool holder and then under high magnification bring the impulse face up to the wheel face to align it up with the existing angle. Or if space allows for clearance you can make a small plate with a close fit hole drilled through it for the anchor arbor to fit through and then clamp this simple fixture into the holder on your cross slide. You can then rotate the anchor until it matches perfectly the existing angle. By adjusting between your cross slide travel and rotating the arbor in the plate hole you should be able to quickly line it up. After everything is set up you can feed the cross slide into the wheel for grinding. If you set it up where it is grinding cross grain to normal sliding direction of the escape teeth then it’s important to polish out any scratches in the same direction as the escape teeth action. Polishing can be done without the use of the fixture set up as very little material will be removed during the final polish.
As William pointed out it’s a good idea to take a few measurements that will help you with final escapement adjustments.
I have to run to town for a little bit so I’m typing this on the fly so I’m most likely skipping some important tips that can be given so I hope this makes sense!
If you have any questions about what I’ve written here please let me know. I should be back at the computer within a couple of hours Jan.
Adios for now,