Theres no way of doing this series in a way that will suit all nations, its too far beyond reasonable expectation for it to be doable.
Whatever the start time is, there will be at least 1 quarter of the globe ruled out because of the local time, it would require considerable dedication on their part to enter.
Accounts will start dipping East of Europe and only really start to pick up at Australia, numbers in that zone will be slim and also tricky to cater for anyway. So if you consider Aus - US - EU is where the majority of racers live and when it could work best for those areas then your looking at +9/10 -8/-5 & 0/+2 for those areas which is a 17hr spread which is doable. 20-22UTC means mid-AM in Australia, early afternoon in the Americas, and late evening/night in Europe. If you move the time 2hrs either direction it either makes it too early for Australasia or too late for Europe, if you switch it 12hrs then it becomes early AM for the America's.
The majority of nations will come from Europe, thats obvious enough, then the Americas, then Australasia, followed by the Middle East, and it should be catered to suit as many people as possible, if its put to public vote then it'll just be decided by what suits the voting drivers best, not the nations, and not always whats in the best interest of the series. 20-22 makes things possible for the widest audience, thats why bott runs at 20utc hardly because arrow likes getting up just before 6/7am.
As for regionals then finals, in theory its a good idea, but in reality it probably isnt the answer. If you stick with the FIFA/World Cup example, its perfect for allowing the best teams from over 100 countries into 1 tournement of 32 nations (IIRC) but the problem is they are professional footballers, and the matches take place in 1 nation with all the players in the same place. They're not expected to field their best 11 at 4am when they have family/work/social lifes to work around, in BoTN thats the reality of it. If you qualify but your best drivers have a problem with getting up at 8am on a Sunday, being home at 10pm on a Saturday or not being out shopping or at the game on Saturday evening, then your hardly the same team that qualified.
It would be far better if we could do it regionally, it'd be much smoother and more flexable, but when it came to taking those regional finalists into the main final your stuck with all the problems it faces if it starts with if theres no regionals.
It'll just require a bit of dedication and sacrifices from most nations (some more than other). Personally i think global events are just too problematic and *just* regional events would be easier and better for everyone, 'bigger isnt always better' springs to mind but it depends what the aim is, better racing or wow factor, IMO the only thing a global series would have over a regional only is a defining answer, whether its accurate/fair or not is easy to argue though.