When you say it smoked out the breather when shut off, not running? The only thing I can think of after shut down would be water vapor. How did the cylinder walls look after pulling the heads? My son had a 340 many years ago. It leaked compression pressure into the lifter valley between the head and the block. Dave Koffel taught me to loosen each head bolt after torqueing and retorque. The bolt/nut will always turn further the 2nd time. It fixed the issue on the 340. Done it ever since. I'm curious why all the tune up/jet changes?
Doug