My method was very simple:
Find a piece of 3/16” mild steel and cut it into a long rectangle with the short side being 3” to 4”. Length of the rectangle will depend on how far you want to place the jackshaft axle from the seat tube.
The idea is to wrap the piece around the seat tube. Use another tube as your working model away from the bike. Apply heat and bend the piece into a symmetrical U shape.
Once the piece wraps around the seat tube perfectly, figure out where you want to center the axle. At that point, use a 1 1/2” hole saw to set the axle placement. The idea, and it will require precise measurement, is to place a 1 3/8” ID x 1 1/2” OD tube (I used fence couplings this sized that found at Lowe’s - I use them as hub bodies for my wheels, too!) through the two “ears” of the metal U piece. Within the tube, you can use two or three sealed bearings (about $6 a piece) to hold a 1/2” rod axle.
You have to get that jackshaft square and true - the best way to lock it down is to weld it to the seat tube. You can also use carefully placed 3/8” threaded rod to squeeze tightly to the seat tube. Would be best to strengthen that seat tube first.
A million ways to do this. Weld the sprockets to the axle or grind out a key slot.