Appeal deadline questions after an unemployment denial - 13 months and counting

My claim was denied after 24 weeks of waiting, and the letter says I have a short window to appeal. There are 5 people counting on me, so I am trying to be careful. My employer's version of events does not match mine, and I have emails that show it. If you have appealed before, what helped you prepare?

I printed my emails in order and wrote a one-page timeline. The hearing officer kept going back to it.