DIY sleeping mat/pad chair kit

For Christmas, I wanted to make Martin a chair that he could use when he goes to the cricket or goes camping.  He's already got a self-inflating camping mat so the obvious chair to make was a "camping mat chair kit": a kind of fabric sleeve that would slide over his existing mat and turn it into a chair.  Finally, admittedly a few months after Christmas, it's done!

I couldn't find any instructions online about how to make such a thing so gleaned information about commercial chair kits from promotional materials and online reviews.  It turns out there were many details to get right.  I'm wanting to share here what I learned along the way so that other people don't have to sew and resew their mat chairs quite as many times as I did in order to get a functional product!

Regular blog readers might want to stop reading here - what follows is detailed and rather long!