Any success, yet?
Because the power of small hot air engines is so tiny (most of them just go, without ever driving anything), I have had to a) minimize friction and leakage, b) use a high temperature and good cooling, c) use a heavy-enough flywheel and get the balance right. Others will have advised of those, no doubt.
You are using metal pistons in metal cylinders, I think. Are they oiled? Although that might help to seal and reduce static friction, viscous drag increases with speed. Are there any eccentricities or offset forces that are increasing the side loading unnecessarily?
If your horizontal piston is heavy, it could be causing sliding friction (you do not need much!). I have found graphite pistons to be the best so far, especially when lapped, because of their low dry-friction (at any temperature), light weight and low expansion (so leakage and binding are constant, unlike with low-friction plastic pistons). Since the forces are also tiny, your metal piston could be foil thin to save weight.
One snag with a heavy flywheel is its bearing friction. On very small LTD engines I have found the drag of sealed-for-life small ball bearings to be greater than that of small plain shafts, so I use the thinnest wire crankshaft that will just carry the flywheel. (True the friction is the same but the radius at which it acts is then smaller.) Would smaller shafts help with your engine?
Good luck with all your experiments! You have a nice looking engine, there, and you will soon get it running, if not already. I bet you then carry on experimenting to make it run better. Everybody does, but that takes longer than making it in the first place!