I have a 1957 Elgin 30 that had the SMB-6A-53 starter motor. I got one run out of it before the push button starter on the front of the cowling loosened up and fell back onto the powerhead and shorted out, cooking the starter beyond repair. I took it to an automotive starter repair shop and the guy tried finding a kit or a replacement but he came up dry. He kept the starter to keep looking and couldn’t find one. I got distracted and never went back for the carcass. I’ve kept this photo on my desktop to rekindle my search from time to time. I’ll be very interested in learning what you find out. 
My main point here is that I think they continued with that starter in 1957.
https://www.aomci.org/forums/topic/removing-tiller-1957-elgin-30/