A four stroke glowplug typically has an extension at the tip to contain the heat in the glow element on the non-combustion cycle in a 4-stroke engine. A hot 2-stroke plug may not be enough for that situation. I have used the OS type F plug and the Fox Miracle plug on my 4-strokes with good results. There are other brands that I have used with success but I can't remember off-hand which they were.

Also, check your low speed needle setting to make sure that it is adjusted properly. If it is even slightly rich, it will cause the engine to quit after a long idle period.