Can you just use a lawnmower starter and a push button solenoid to build a starter like the Burris starters. I've never really looked close at one of the manufactured ones. Any help from someone who has built one
No. Those starters require compression release to work. Subaru starters work great. That is what I built mine from. Legacy Subaru starters are gear reduction.
No, they will not work. Think about this........ Ratio. How many teeth are on a starter gear vs. the number of teeth on a flywheel of a lawnmower. And as mentioned, lawnmowers have a built in compression release. Historically, we've used starter motors ranging from 6v Ford starters on 12v to the gear reduction starters popular today. But notice all the best starters are basically from automotive backgrounds.
Grind a flat so the set screws in the extension have a place to grip. I used to make my own extensions out of alum stock with Torrington 1 way clutching needle bearings, with a humk of drill rod, that had a snap ring groove on 1 end and a thrust washer, and a hunk of 5/16" allen wrench brazed in it.