I have researched and fixed a Honda GC190 air cooled engine from a wood splitter, that used a synthetic oil. The original problem was a stuck decompression mechanism on the belt drive timing gear. Further observation was oil as black as spades, however the owner was very diligent in changing oil and documenting it in his cell phone. He was really PO'd when I suggested this normal human error. I changed the oil to 30W as recommended by the manufacture. I then sprayed the decompression mechanism with "PB Blaster and it went to working correctly.
I then discovered he was using a synthetic oil. Further research on the web revealed ,from an expert, that "synthetic oil was not recommended for an air cooled engine, as it coats the cyclinder wall and with the next explosion cause carbon to get to the rings and causing further "blow by" and contamination of the oil.
Synthetic works great in a car engine but not air cooled engines. Use what the manucture recommends" 30W or 10W30 for cool weather".