Greetings from RojoLand!
I've owned a 4000DS Mk-II since 1979, purchased new. When I was given the 4000DS (mark one — grin!) and noticed its lack of built-in reel locks, I was a little dismayed. But it's relatively trivial to change out the reel tables, IF you can find the later ones. They turn up on occasion, but for more $$$ than I want to spend right now. I'm just living with the rubber reel locks. I'm used to them, since my Teac A-4010S and Concertone S510-R both use them as well.
Hard to figure why the tape you have appears to be "between-speed." No oddball sleeves were ever made for this deck. Perhaps the previous owner was after some kind of effect, or he monkeyed with the deck in some way. (Is the music recognizable in any way?) Fortunately, weirdness on tape can be bulk-erased and the tape is good to use if undamaged. Speaking of tape, you'll note the Normal/S.R.T. switch. "Normal" is Scotch 211 (per the owner's manual) and similar tape. (211 is the same as Scotch 176 and Scotch Highlander 228.) "S.R.T." means Akai's Super Range Tape (not easy to find), or Scotch 206/207 or the like. Maxell UD is great on this deck; I recorded many of my radio shows using UD 50-60 (at 3-3/4 IPS, yet) and they sound today just like they did 35 years ago. Give Capture 914 or 930 a try (from Splicit.com). There's also MDS-36 from ATR Magnetics; it's supposed to be equivalent to Maxell UD 35-90. Don't run older stuff like Scotch 111 on this rig.
Take care,
—
J. E. Knox "The Victor Freak"