the exhaust is actually touching on the inside. so that could be it
Sounded very familiar to me. A couple of days ago my 4/4 Kent Mog started making a similar noise on start-up when the idle is uneven. Looked underneath, shook the muffler, all felt firm. It continued to make the noise on first start up. Today I got underneath and had a good look and found the steel strap from the bobbin in front of the muffler to the chassis had cracked (broken) at the chassis. The noise was the broken bit attached to the exhaust pipe hitting the chassis.
I think the steel strap will have to be ground off and a new one welded on. Just welding the break will probably not be a lasting solution. You might have a different problem i.e. as you've suggested it could just be the exhaust hitting the chassis but have a good look. It took me some time to spot this.