James VI could proclaim himself whatever he wanted but there was no legal basis in his titles, just his personal desire to unify the Kingdoms. It's perhaps evident in the fact that it took another hundred years (and it was a really half assed union where even the laws were separate). to demonstrate how unwilling the two nations were to combine. If he actually was King of Great Britain then the regnal number for William and Mary would have been I.
I agree that they can't have both but I wouldn't be surprised if they tried it anyway.
1. The Highest Regnal Number (works with both England, Scotland and Great Britain)
2. Multiple Regnal Numbers
3. Great Britain Regnal Number as of 1605
4. Great Britain Regnal Number as of 1707
5. English regnal number
6. Scottish regnal number
Two is weird but possible
Three requires retroactive fixing
Four would be weird but again clearly Mary and William didn't think it was a new Kingdom, whereas after the Acts of Union it clearly is. Potentially look for Spain for comparison, Spain was apparently not a reason to restart on regnal numbers but I think the choice by Alfonso was particular to his situation, he wanted to make it look like a real monarchy again and having a big number imports history.
Five will annoy the Scots but you can delay it for 300 years potentially
Six will annoy the English and requires careful name selection though for a while it may look like any of the other options