If logs are cooled with lake water from heat exchanger, how could exhaust get into the freshwater/antifreeze side?
Heat exchanger should have a "radiator cap" ~10 lbs maybe? the exhaust system would have to be in excess of 10 lbs of back pressure (if there was antifreeze in the logs) to have exhaust entering the logs.
Most likely a blown head gasket between chamber and water jacket. A pressure check of the (antifreeze/freshwater) side of the system will tell.
The head may also be cracked, but that is not as likely.
Good luck
Daniel