Y'know, everyone motivates themselves differently. But if I were in your shoes and started despairing that the thing would ever run, I think I'd try gasoline (or ether!) just to make sure that the rest of the engine is functioning correctly. Once I'd verified that the only salient problem is gas regulation, then I'd attack that, confident that it was the one remaining barrier to joy.
You do need a throttling carb, a barrel throttle type RC carb will work fine with about a .188" bore in the barrel. To reiterate, you need a propane regulator of about 4-5" water column output pressure (Weber Go Anywhere portable gas grill), a JH demand regulator (DR), and a throttling type RC carb with a needle valve at the carb. Keep in mind, the discharge side of the DR remains at 0 pressure at all times except during the intake stroke. On the intake stroke, this side goes negative pressure allowing fuel to flow to the carb.
Also, on the intake stroke the intake valve should give an audible "buzzing" noise. If not, you should reduce the spring pressure a little at a time until you get this action on the intake valve. You may not be getting adequate cylinder fill due to a short intake period.
Butane regulators (non-adjustable types that give LOW pressure for caravans, etc.) provide a lower pressure than Propane regulators. But you are getting too much gas. The only guy I know who has really mastered gas says his answer (as a watch maker) is a TINY jet - 0.25mm or smaller - with the finest sewing needle he can buy, in a tap using a 40 or 50 TPI thread, and then the valve is only just cracked 5 or 10 degrees, or so... depending upon the engine. But his are mostly 1/2in bore by 1/2 in stroke or smaller! He doesn't rotate the valve knob, but has a technique of giving it the tiniest tap on one side or the other - he says to adjust the mixture by only a couple of degrees of the knob rotation. - But he doesn't use a gas regulator, just "tin pressure" butane at 10~15 psi. He is a bit of a genius. He has even tried the jet from a cigarette lighter, but said he preferred to drill his own - down to 0.1mm I think? - the drill was only about 2mm long on the end of its shank! But I said he is a Watchmaker... One of his freelance hit and miss gas engines attached.. The wood base is about 5in long. The gas valve is on the right - just above the fuel tank. Hit and miss is shown lower left.