That is a long message! My old copy was dated 12/10/68, which struck me as being too late. Perhaps people felt a December date was more fitting since TC had joined the band by then; nonetheless I think a November rehearsal makes more sense, given what we're hearing. (If anything, I think this is earlier than November, but can't prove it.)
TC has said that he could join the Dead for brief periods on leaves or 3-day passes. (He would not have needed to go AWOL.) I don't know how generous the Air Force was with those, though, so it's unknown how frequently TC could have visited before his discharge, which was on 11/22/68. This session could be the one time all fall that TC was able to rehearse with them. As for using a studio to record the rehearsal, I suspect a couple factors were involved. One, the band at that point just didn't care how much time they spent in the studio - the number of months they spent recording & re-recording the small batch of Aoxomoxoa songs, heedless of debt, indicates that. Also, they may have wanted the session recorded so TC could play it back, to help with learning the material. You can hear someone ask the engineer after Lovelight if they're recording. (And, as you suggest, they may have hoped something useful for the album might be recorded at the session - it doesn't sound that way to me, though.) We know, for instance, that on 9/21/68 they used the studio to record a jam session with a couple other guitarists (likely Vic Briggs & David Crosby), so they were by no means concerned about the cost of studio time. So Pacific Recording remains the most likely place. The mix changes from time to time, so I doubt the session was meant to test the mixing. I think the engineer would have taken more care if that were the case. The mix is sometimes quite poor. I guess it's a Vox Constanten is playing here? (When he joined the band, for a brief time the band had two organs - Pigpen on a B-3 and TC on the Vox Continental - but the Hammond was repossessed shortly thereafter.) Deadbase does list a number of Pacific Recording sessions for Aoxomoxoa, from Sep '68 through March '69, but I believe these are incomplete. There must have been more sessions that aren't listed. They do illustrate the Dead's leisurely pace in the studio, though - note that all of the Sept & Oct sessions are spent simply doing four songs (two of which are then dropped)! According to McNally, the 16-track didn't arrive in the studio until around Christmas '68. I think that's far too late for this rehearsal to plausibly be a 16-track recording. (Lesh in his book just says it came in during their midwest tour, but he isn't being precise, and makes several wrong statements about re-recording Aoxomoxoa.) So I strongly disagree with this session being taped on 16-track. And for this tape to be from January '69 is flatly impossible. Just a brief comparison of the Dark Star & St Stephen here with versions from the Avalon (1/25 or 1/26/69) will make that clear. The playing was simply far more advanced in January - Stephen, for instance, has a more extended intro and an added jam in the middle by the Avalon shows.