Ah, thanks for pointing me to where I change change the timezone. This makes it easier, and my request look fairly useless.
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subtract the next quarter hour time from that and you now know how much time is left until the changes get pushed out.
Correct; but that's the time left from the last modified time, and not the current time! If you were to browse away for a few minutes, how would you calculate how long until the next generation? You can't (without using your system time), because all you have to go by is the records last modified time. That was the situation I was in.
However(!), now that the last modified time and my system's time are running the same timezone, I can now calculate exactly how long it will take until the next generation.
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But it'd be even easier if there was a big fancy JS powered countdown timer.
Bingo!