Have you tried reaching out to your SA directly? I saw my SA over the weekend without a problem, I reached out to him on Wednesday for an appoint that Saturday via email and he asked me what time I'd like to come in (so it sounds like there are more than one timeslot available). Anyway I ended up going in at 11am. The store did seem a bit busy when I first got there, they also kept the door locked and so the doorman would have to let people in. After my appointment, while waiting for a cab outside, I overheard this couple trying to do a walk-in for bags, the doorman went in to "check" and came back after a minute saying that the handbag inventory is low so they're doing appointments only.
For reference, I checked out the meatpacking store about a month ago to exchange a scarf for a different CW and tried walking in. The doorman there said it was appointment only but also went in to "check" and eventually came back and told me they can see me in about 45 min. I went to have lunch across the street and got a call from the store to schedule my impromptu appointment. In the end I was seen by someone about 1 hour after the initial walk-in.
I'm not sure if this information helps at all but I hope you manage to get an appointment soon!