The letters from the tribunal are just templates and don't really mean much.
In practice, the tribunal gives appellants up to two reschedules, no questions asked, and you can actually upload evidence as late as the day of the hearing.
This being the case, just want and see what the council does. If they don't upload anything at all, you win by default. If they upload their evidence when you only have a few days left (I've seen them upload evidence as late as the day before), just phone the tribunal call centre and ask to reschedule the hearing, you can push it back by up to 28 days and they'll do that while you're on the phone. You then have a month to prepare for the hearing.