Brompton uses 112mm.

Cold-setting the triangle doesn't affect the fold, but it must be done properly — the right stay is slightly more curved outward, so the ratio must be preserved when pulling the stays (wrong way to do it).

It'd just be a lot easier if Brompton simply sold it as an option. No need for DIY.

I don't know much about derailleurs, but maybe one with a short cage (what's the widest cassette they can take?) + dual crankset in the front would offer a wide enough gear range for touring.