The tram got to just inside the door at Victoria station and stopped. There was a tram in front just sitting in the platform not going anywhere. Turned out this was due to not having a driver, and it was sitting there waiting for one (you would've thought they'd do this at a terminus rather than in the middle of three routes, but whatever) so while sitting on the tram waiting to get to the platform, the 10:21 left. Well okay then. New plan. The next train to Leeds was the Selby-bound train at 10:48, which would get me to Leeds for 12:12. Still plenty of time to get to Carlisle on time, which is the important bit. I can't cancel my hotel if I don't do it before 12pm, so as long as I get on a Carlisle-bound train, I can safely make it to Newcastle, regardless of how late it is.
So here's the updated timetable with delays and changes as-of writing this post on the train to Leeds:
|Depart Time||Depart Station||--||Arrive Station||Arrive Time|
|08:50+5min||Crewe||--||Manchester Piccadilly||09:44+10min (arr: 09:54)|
This still gives me over half an hour leeway at Leeds, which means I should still be able to make it. We'll see how the day continues.