I've now had a look for both types of starter dogs and taken some new pictures for comparison.
The middle section of part no. A-139-2 measures approx 1/2" and the older part no. A-139 measures approx 9/16" (from the early Model L engine I have).
And here are the two different types of starter dogs shown on an early flywheel (from a Petro Chug-A-Pump approx engine s/n #14000).
And the same starter dogs shown on a slightly later flywheel (from a Tiny Tiger approx engine s/n #35000).
If the information from the 1962 parts list is correct then the starter dog part no. A-139 was last used on engine no. #015997, after this they should be part no. A-139-2.
If you need the later one (A139-2) then I have a couple of used spares, I don't remember thinking I would need many so didn't buy any spares from Webhead, as I said before I don't have any spare of the older ones (A-139).
David