Richard, I have the E3 screen in my FM3a and a spare Beattie screen similar to the K3, but with grid rulings. I am tempted to try this in my Df, hence my R&D.
The FM3a handbook on Page 47 makes the following comment about focus screen interchangeability between the FM3a and the older FE2 and FM2n (1/250th flash sync) cameras:
"K2, B2, and E2 types for the FE2 or the New FM2 (the latest version with 1/250th sec flash sync)
can be used with this camera (i.e. the FM3a)
without exposure compensation. K3, B3, and E3 type for this camera (i.e. the FM3a)
can be used with an FE2 or New FM2 camera, no compensation required."So they are interchangeable. Subjectively the K3, B3, and E3 types look a little brighter to me than the K2, B2, and E2 types, but obviously the metering is unaffected according to Nikon.
Pages 46 & 47 from the FM3a manual are attached.
EDIT: Also similar pages for the FM2n and the F100 film cameras. Nothing about screen changing is mentioned in the manuals for the D200, D700, D810, or the Df. Have not looked for the D* series of cameras. The subtle differences between the tabs on the K, K2, and K3 screens can be found in these pdfs; ditto for the tabs on the B and E type screens.
I have added this super useful table to the site. I am going to buy an old F6 screen, maybe later