By Jove! I think, at last, you may have cracked it gentlemen. Good work!
Those two machines appear to bridge the gap. The Allwin Supreme provides the maker's name and although, at first, it doesn't look much like the other mystery machines, it has six visible distinctive features in common with the Allwin: the unusual shaped gallery back plate, the diagonal-slot coin entry plate, the long hinges, the diamond shaped coin cup surround, the payout knob and collar, and you turn the handle clockwise for a win.
The Allwin, with its arched door frame, is more obviously from the mystery stable and has most of the typical, features.
I would imagine these are both early examples of the type, the Supreme being the earlier.
Another notable thing about these machines is that the cases tend to be of beech or some other softwood or, in later examples, plywood. The Supreme doesn't look like oak.
As such, Morris Shefras allwins were the nearest match. They're unusual in the use of softwood cases (and later, ply) and they have the clockwise payout. It didn't make sense, though, that Morris would be making two similar but distinct sets of allwins, one with his name on, the other without. But it does make sense that the two Shefras brothers with their separate companies produced a set each.
Of course, it's possible that Philip just distributed the Supreme, but until someone can persuade me otherwise, I'm referring to our mystery machines as Philip Shefras allwins.