Brad - looks like you are doing a fantastic job with this. Once complete, the helicoil will be better than new.
Drilling "plumb" holes for tapping purposes, another possibility:
I have a milling vice attached to the tailstock of an older lathe. Setup can be time-consuming if one is only going to do one hole, but if several are needed......
Once the hole to be drilled is properly set in the milling vice, leave the tailstock slightly loose, so it can slide on the table.
I then place the tap in the headstock, UNPLUG the lathe, guide the tap into the hole, and turn the headstock by hand. The tailstock will slide, allowing a perfect thread to be cut. Don't forget to oil the tap.
And Brad mentioned the 10-32 was the smallest thread repair he has attempted. Before we got a set of "slitting saws" (to cut slots in metal) for the lathe, we repaired several throttle shafts with 6x32, 4x40, and even 3x48. Difficult, but doable. Now, depending on the overall condition of the shaft, especially how the arm fits and the wear where the shaft contacts the throttle body, we will either install the helicoil, or machine a new shaft.
Lots of enthusiasts overlook some really top quality older tools. We bought a mid-1950's Sears Professional 12 inch lathe with some issues a few years ago for $400. Turns out the PO couldn't understand wiring diagrams and miswired the reversing switch. A new reversing switch and lathe works perfectly. Lots of really good (but old) made in the USA precision tools out there just wanting a good home.
Jon.