I don't know if this is true for this brand, but I'd always assumed that Omega uses the same system.
The only way to improve this is to have another crown position to adjust the date independently... so 4 positions (winding, time zone set, time set, and additional date set).
I know how it works in the genuine Omega:
To independently set the hour hand, pull out the crown to the date-set position. Rotating the crown up or down will move the hour hand clockwise or anti-clockwise (depending on which way you turn the crown - necessary for when you go "backwards" from say New York City to Hawaii/Lanikai for example). In this adjustment position, the minutes and seconds continue to tick away as if nothing has happened, which means you can seamlessly go from one time zone to another (unlike the ETA 2893 which requires that you view the GMT hand as the current time, unless you re-set the watch, not very convenient is it ?)
To change the date, you have to advance the hour hand to midnight. This can become monotonous as to change from one day to the next requires a complete 24 hour cycle with the hour hand. Luckily, on the genuine, this is pretty quick-ish.
To adjust the "GMT" hand, you have to go to the usual timeset position and adjust the minutes as per usual. This should also "hack" the movement and the GMT hand will move as you advance or reverse the minute hand.
Hope this helps!