I share your opinion about Midas and Meineke, and don't like the short lived parts
they use. The one piece muffler might be OK if there's no junky extra parts
to rot out? Maybe you can get a new muffler from them every 26 months under warranty? Maybe they'll want to weld it in and have another bag of sad surprises
attached to their warranty?

Permatex has a large product line, see this:

http://www.permatex.com/products/Automotive/specialized_maintenance_repair/exhaust_system_maintenance_repair.htm

The directions are vague for the Muffler Tailpipe sealer Item #80335
They say to wet the surfaces with water first and then assemble.
Then clean up with water before it dries.
No clue about waiting for it to cure.

I think it's worth a try.