Hey. Let me know how you go finding a 4-jaw to fit. As for the bump tool - the allow used for the snapmaker is non-metallic… found that out with the dial indicator…makes life harder - so plan for bolt, OR bolt a steel plate so you can then use magnetic. Rotating is hard… best I’ve found so far is to labouriously press the 5 degree rotate button. I thought of creating a job with a 20cm OD so the tool sits out the way, but there’s no way to start/stop.
Thanks @edf - Yeah - not sure on facing the jaws yet - there seems to be enough (too much) slack in the mechanism, so either some copper pieces or similar might be the go (not sure the jaws can put enough pressure on the copper to deform suitably, like in a “real” chuck - maybe I can put them, pressure and tighten, then loosen and run a reamer through to get some degree of parellelism before closing the jaw on work stock?. I think your idea of a new chuck might be the best (either a real/better 3jaw or 4jaw). My lack of knowledge of the different chuck faceplates limits me, so let me know when you find what faceplate they’ve used (if they’ve used a standard!), and/or adapter plates you’ve used, and your recommendations when you get there. 
When I make my new tailstock holder, I’ll post the plans. The live centre seems OK, just the holder and bolting to the base seems “under thought”.
Also see my new post - Rotary Tool concentricity/runout issues with the chuck itself - #2 by Doogs75 - for more issues that I’ve run into…