Well I have not gone off and died but I have been tied up with many other things. I got back to thinking about the poor performance of my engine and came up with an idea. I am thoroughly convinced that the engine is stopping because of "heat death" That is to say that the engine runs only because of the temperature difference of the high and low temperatures in the engine and that eventually the cool part becomes as hot as the hot part (or so nearly so) and there remains insufficient temperature for the engine to run.
Aluminum has such a high coefficient of thermal conductivity that it appeared that the heat of the flame was being transferred to all parts of the cylinder and thus there was insufficient temperature difference and thus "heat death" the thermal conductivity of stainless steel being lower, the engine should run longer with a stainless steel cylinder.
It occured to me that If I could reduce the heat flow from the flame area to the rear cylinder bore things should work better and that is what the heat shield I attached at the flame hole proved, but that was not enough.
Heat conductivity is proportional to the cross section of the conductor, and the cross sectional area of the cylinder wall was approximately 0.825 square inches. If I could reduce this area the resistance to heat flow to the rear of the cylinder would be increased and the flow of heat there would be reduced. So I cut the grooves between the cooling fins .188 inches deeper. This left me with an 83% reduction in heat conduction area. and a remaining cylinder wall of about .050 inches.
Getting a hold on the cylinder while maintaining access to the grooves for recutting is a bit challenging. My tail stock ram lacks sufficient length to support the free end of the workpiece and still move the grooving tool to the grooves on the outboard end. So I decided that I would try just recutting the front 3 grooves and leave the extra mass at the rear of the cylinder. Due to the short grip of the chuck I made the cuts gently, especially since the cut would be an interrupted cut due to the presence of the valve pushrod hole. More fussing with the setup would allow me to recut all the grooves but this was an experiment anyway. After dialing in the 4 jaw chuck I proceeded. The cylinder is shown back lighted in the second image and the deeper fin cuts are obvious.
This revision made an even more greater improvement than the heat shield I added behind the flame.
Based on this experience, my view is that the heat conductivity of aluminum can have a major influence of the performance of these flame licker engines and that when alternative materials are suggested, that their lower conductivity with respect to aluminum may be advantageous for some designs.
Cutting all of the grooves deep and adding fan cooling would probably be very effective.