The split nut crumbled under my fingers and was finished off by a screwdriver. If the bolt head is captive then am I right in thinking I have to drive the bolt out backwards or grind it away? What if I drive a chisel in between the two flanges - and is this better done with the rubber hangers off to encourage it?
I had the same issue. Since I was replacing the back box with a new one, which came with new bolts, I just used a small hacksaw to cut the bolt in half between the backbox and centre pipe.
Obviously, don’t do this if you want to reuse that bolt!
Cut it off and drill it out for a suitable exhaust nut and bolt replacement would be what I would be doing.
I wouldn’t drive a chisel between the two flanges, as I suspect it would bend/damage the flange and just make the job a lot harder and more expensive. 
Ah, must have missed this thread.
Welded on? Could Mazda have thought that the back box would outlast the car and therefore would never need replacing?
That is a strange one. The head end looks like a stud but surely not enough metal thickness in the flange for splines to hold to?. Flanges look very clean, so the nuts must have been the sacrificial metal for corrosive activity. Not much of that nut left; If you had some sort of grinding tool to work at the base where metal remains, I think it/they would just let go.
Are you scrapping the backbox? Guess that is the part where the threaded parts sticks through? If so probably easier/quicker to cut through the lipped part of the flange with a thin disc to hit the threaded piece at its base and cut it off square. I’d guess the head end on the centre box flange has to be welded on. You will need to drill from the back box end and see what if left of those heads.
The head of the bolt is the back box end. There’s hardly room to get your fist between the back box silencer and the flange hiding the bolt.
I can’t get the bolt to spin with big mole grips after a couple of days using Plus Gas and heat.
Thinking of hack sawing, then grinding off the rest of the thread - then drilling out what I’ve got left.
I hate being beaten by a simple nut and bolt.
If you have got it to turn, cutting the head off would presumably relieve the rest?
Can you get a cutting disc onto each side of the flange to cut in and slice the heads clean off?
Hacksaw would work too but probably have a few blisters at the end of it.
Might be easier to work on if you disconnect the exhaust at the engine downpipe and work with it off the car.
Support the mid pipe and give that flange some gentle persuasion, hammer or drift in-between the flanges. Leave the hangers in place on the back box.
Is it just one nut chewed up or both?
This is the mid pipe freed of the back box, if replacing the back box you’ll need new nuts/bolts anyway as the original bolts are fixed in the flange of the back box.
Thanks for the suggestions.
A suddenly defrosted freezer a couple of feet from the back bumper (replacement on it’s way) and a son moving house in the next 48 hours is going to cramp my style in the back box department - but give time for the Plus Gas to do it’s work.
I’ll have another pop at it midweek.
Yep had similar problems with fridge/freezers this week. My son’s packed in only 14 months old, out of warranty of course, our emergency freezer (not used by us) delivered to him late at night. The useless lump of a freezer now disposed of and the new installed, + extended warranty.
I’ve got the back box off now.
I was able to hack/angle grind half the bolt that extended beyond the external (galvanised?) flange. The rest of the bolt was held in place by a conical dob of weld. This was attacked with a grinding wheel and held until the last 2mm when it came off like a steel washer. The round headed bolt appears to be captive in the back box.
I posted a pic previously of the exhaust tip protruding from the rear of an NC1 sport. The NC facelifts have s slight different design rear lower bumper valance.
