The problem with custom deadlines and RescueTime is indeed with RescueTime's API (not to throw shade on them), but their API aggregates data by day, so we don't have a way to ask for the time spent between, e.g., 02:00 and 01:59 on the following day.
Furthermore, changing your Beeminder timezone won't help with this problem, because even if we wait until 2am to call your goal derailed, RescueTime is not going to count the time you spent between midnight and 2am for the previous day, so if the time wasn't spent by midnight, it won't help.
You would have to convince RescueTime itself of the altered timezone, which, unless I'm mistaken, would probably involve changing the system clock on your computer, which sounds like it would be highly inconvenient in general. (I could well be mistaken. Maybe they've got a premium setting that lets you do a custom end of day? Enlighten me please if so!)
The same argument applies to Misfit and Fitbit. I can't think of others off the top of my head.