(This post gets a little technically dense; sorry about the brevity. ETA: typos corrected!)
I was mulling over the
Egerton Gospel, as I do from time to time, trying to think of where it might fit into the HSH. I had become particularly interested in its mixture of Johannine and Synoptic elements (which were always triple-tradition elements). I'd never been able to fit it into the diagram before, but what if it were a kind of proto-John? The "Johannine-only" elements would then have been taken from the Signs Gospel; the synoptic triple-tradition elements from the original Gospel of Mark, i.e. Secret Mark.
This would have been a slightly complex idea, however, because I would then need a reason why the canonical Johannine redactor either edited out or heavily rewrote the synoptic elements. This wasn't an impossible idea, but I didn't see anything in those elements (the questioning of Jesus by his opponents, and the healing of a leper) that seemed to require special treatment by a Johannine author. So this remains an intriguing idea, but I don't think it's the best one.
I then turned to the Q side of the diagram to reconsider placing it there.