I also have a small Michigan guitar, (hello Giles, hope you got my email, I see you found this thread!), it's a flat-top with a floating bridge a small plaque on the headstock says "B & SL Sole Agents". My dad bought it second-hand many, many years ago, I learnt on it, borrowed it about 10 years ago and he hasn't asked for it back yet!

I've seen a Michigan resonator guitar, almost exactly identical, except for being a resonator guitar, and a Michigan mandolin, all with the same headstock, unfortunately looking fairly unplayable, on the wall of a pub in Slough.

Apparently Michigan was a brand name used by a British importer for instruments made in East Germany in the late 50s/ early 60s.

Mine has seen some action (and been repaired for some very nasty cracks in the body), but sounds like nothing else, it really chucks out a lot of noise, great in sessions. I've used it for a couple of acoustic gigs, but it needs a bit of work on the frets to get it up to scratch.