GOING WAY BACK!!! on the 340's
IF the motor still has the factory steel shim head gaskets, they were known to blow out the bottom of the cylinder between the block and head. Why?? because there were only four bolts per cylinder and the head bolts / gasket lost torque over time which resulted in a cylinder leak that sounded a lot like and exhaust leak. This issue typically appeared on the center cylinders around 80 to 120K miles. if the motor has been opened up over the years it is probably not the cause of the noise. But wanted to throw it out there.
Also wanted to say that if you wire the heat riser open
(assuming it might be partially closed) it would eliminate the back pressure forcing the noise to become prominent. unless of course the exhaust is restricted elsewhere which based on the description is doubtful