Just do what you think is best, normally I would say that it SHOULD be easy to have at least 2 rounds of a draft off the clock, however we know that's not so.  you also have the guy who wants to trade his pick, which he has every right to do but if he doesn't get a good offer or is waiting for a better offer that can hold things up.  I remember a guy had the #1 pick in 1907??  (Walter johnson) posted that he wanted to trade the pick and then didn't respond to any offers.

But back to your original problem it not time zones , its working hours and whether or not you have access to this web site all day long.  Thats what prevents people from joining progressives  because they maybe unavailable for a draft and they really can't trust a proxy.   Even some progressive league commishes are unvailable during their own drafts.