Some have posted that Chief has the BME-110 in stock.
Keith also has the BME-110 available without the ignition.
I wasn't on his list, but he said he could sell me one without ignition a few weeks ago.
He is shipping engines. You'd have to talk to him to find out when you will get yours if you are on the list.

I bought a used 3W-106 instead of the BME. I like 6 bolt hubs and I already have a spare ignition, spinner, mufflers, and props for the 3W. I've had good luck with a pair of older 3W-100 motors. I hope the 106 proves equally reliable.