So, as an addendum to this, I finally got my EbyG Sheraton set up properly (about 25 years late!) by the excellent Fleetcroft Guitars
and the tuning is now rock solid - I've been hacking at Comfortably Numb which has massive bends in it and it is not budging a cent.
I've started playing again after a hiatus of about 20 years, so I'm basically learning again from scratch and it really is a lovely guitar.
By chance, I was in Andertons yesterday and had a look at a modern Sheraton II and the quality is nowhere near what these old ones are - mismatched wood on the sides and top, crappy stick-on 'E' on the pickguard, wonky binding on the side of the fretboard, poor inlays.
I really think I was damn lucky to buy such a great guitar all those years ago and definitely think these will become collector pieces in the future.