Dawley Aviation in Wisconsin is known to do a good job refurbishing these mufflers. They charge $225 if they can reuse the shell and $298 if they can't. The problem is that with a two to three day turn-around, sending the muffler there would require either use of extremely costly overnight shipping or accepting the idea of N631S being grounded through an extra weekend.
You can buy a brand new muffler from Cessna but they want about $2,000 for it (I kid you not). However, a high-quality aftermarket replacement is made by Wall-Colmonoy. Their Nicrocraft line of exhaust parts is carried by Aircraft Spruce and this unit (part number 0750161-89) can be had for $332.95 plus shipping. This may cost a few dollars more than the repair but the timing will be better.
"smoking rivets" have shown up there and Cessna has a service bulletin (number SEB03-1) covering the area. It calls for increasing both the number and size of the rivets. But the plastic end caps are cracked and likely not salvageable, so they'll be replaced. The image at left is from the service bulletin, showing the area in question.
I'll be stopping off at the airport tomorrow morning, of course, to see what new things are in store.