Hey this is pretty cool, I looked in to building one of these years ago but never cut chips. I think if you just turn the Piston flat and machine the head out for an insert with a flat bottom you'll be able to get it running. My thought was to use a glow plug from a rc airplane motor instead of adjust compression.
Doing a bunch of research into the lohman, it looks like you use the compression adjustment to get it started (high comp) then you turn it down to lower comp once it's warmed up and the rpms can then increase, controlled by the throttle. My original goal was to run on veg oil but I got cold on the idea once I realized I would have to mix it down with kerosene or something. Also you don't have to look to far for ether or methanol to cut down oil and make it light off easier, I have a torpedo heater I've had good luck running on waste oil mixed with gasoline instead of kerosene. Even 10 percent gas added to diesel or kerosene will make it light off really easy.
A guy I worked with put hydraulic oil in a Honda pressure washer once and it ran surprisingly well, in fact we couldn't figure out how to turn it off.