The only thread I'm familiar with is 1.375 diameter, 24 TPI. This is the BMX style, yes. But I have found multispeed "clusters" that fit on the same -- just don't know what they are named. Bicycle rear wheel hubs come in a gazillion designs -- or so it seems to me. I do not know what will fit what.
My adapters look just like the Miami Sun trike adapters on that site. Probably the J&B parts I mentioned.
For shafts, I use industrial keyed shafting. Not cheap, but a real problem-solver.
You describe your jackshaft as having two inputs and one output. Does that mean you are using a differential? If so... why? I have had great luck with separate drives on each side. Can help you steer in sand, too. And diffs are so prone to failure.
I have a professional engineering drawing of my adapter. The engineer released it to the KSR community. It is in PDF format. I would have to experiment a bit to remember / figure out how to post it.