You kind’a answered your own question. I believe that if you want the app to behave correctly for all users in all time zones, you cannot assert a specific time on the data set. Instead, you must allow the system the latitude of shaping the data in concert with the user’s browser locale.
I’ve always advised against the use of fixing the data to a specific timezone. This is contrary to good database design and especially problematic when workers exist in different time zones. There are exceptions to this rule, but not many.