Hello Steve Dalphonse,

Looking at 'The Filling Station' expanded picture of their exhaust system item: EX-29-32, it shows a stud at the end of the head pipe. Is this the stud that you refer to? I have not worked on the exhaust system on these cars. To guess, I would think that this stud anchors the muffler to the head pipe inside the muffler. If so, and the muffler appears to be loose at this location, maybe your mufflers stud hole mount area is rusted away. Just guessing. An exhaust stud and nut inside the muffler, I believe, may be frozen and a lost cause to try to tighten. A strong light and close inspection of the area is suggested. An alternative may be to look at the front of the loose muffler where the head pipe enters. Could L-brackets be attached to the face of the muffler (spot weld, rivets, self tap screws, JB Weld) that surround the head pipe and held to the pipe with a bolt-on clamp? That may tighten up the muffler. If L-brackets make for an ugly installation, with imagination and metalworking, a custom clamp-shroud might work. This may not be what you are referring to, if so, disregard.   

@harry-truppner Yes the stud anchors the muffler and forces it forward to seal on the bevel of the exhaust pipe. I am hoping to find someone that may have had the same issue and have some tips . One thing I may consider is a band clamp at the muffler inlet.