I am not a professional mechanic either. I could see how sitting so much could have left some deposits in the engine. Maybe the previous owner did not change the oil every year and let that old oil set in there through the winter. Maybe there are some deposits on the valve seats and that is what is holding the valves slightly open causing the leak by. Are cylinders 3 and 5 on the same side? If so, I would pull off that head before taking out the entire engine.
I have never heard of BG products before. I have always been nervous about oil additives. Fuel additives scare me less. But, at this point it could be worth a try before going to all the trouble of pulling off the head. Maybe the BG will clean off some crud somewhere that is not allowing the valves to close fully.
The bearded mechanic on Gas Monkey Garage had a good quote one time. He said "an engine wants to run".