I had reached out to the help desk a couple days back, and just received this response back to my inquiry about wait times:
"
Dear Applicant,
The message "No available appointments" does unfortunately mean that there are no available appointments for the chosen visa category at the chosen Embassy/Consulate.
Please be aware that certain visa categories are very popular and the available slots fill rapidly. As the amount of appointments made available are at the sole discretion of the Embassy and the consulates the only advice we can provide is to keep trying to find an available appointment.
Thank you,
The Contact Desk Support Team."
Now I'm not a lawyer, so my ability to read between the lines isn't great, but I think I just got told to "Sit down, shut up, and wait to get lucky like everyone else" in the most professional way possible lol.
But yeah, what I basically get from this is waiting over a month for an appointment opening that may or may not come is totally normal for this consulate, and they have no plans to change this or help in any way.