I’ve only had one dispute but that required the period to elapse before it gave you the opportunity to progress further – it seems to have no regard to whatever happens up until then.
My case is similar in that I disputed something with a seller, the seller made it clear they didn’t want to compromise/negotiate over it so I raised a dispute, had to recontact the seller to confirm their stance and once the deadline was met I could raise it to the resolution centre.
I found ebay were very supportive in my case as a buyer (although it seems a bit hit and miss at times).
My advice would be wait to 20th Oct and then raise the dispute to the next level.