The Effzett is for the initials F.Z., Fritz Ziegenspeck the founder of D.A.M.
(Ziegen is "goats" in German, hence the goat trademark).
http://dam.de/html/e_dam_geschichte.htm
Since he was manufacturing reels in 1902, and the reel bears his initials, I don't think he bought the design.
I have had one of each style. The 3-pillar reel is very nice - it's made for RHW, opening the back of the spool to your thumb for drag. (Sold it to a friend who was fishing it a few weeks ago and used that thumb slot drag on a big catfish.)
I've always though the 4-pillar reel was an earlier design (because the 3-pillar is such a cool idea, it had to come later, right?

). Also the level of finish detail is nicer on the older reel. One of those things that had to be given up when competing with cheap Milbro brass reels.
I don't remember a washer on my 4-pillar reel, but those are the kind of pieces that easily get lost over 70 years. Even my 3-pillar reel had the wrong thumbscrew with a round-holed washer underneath by necessity. However, there is no question, my 4-pillar reel did have the DAM trademark on the face plate. Maybe it's been rubbed off on yours - I do see some pretty big scratches?