Honestly, this would ruin the game.
Do you know how much time professionals spend playing Go? there's a reason.
I'm sorry you encountered someone who was stubborn, but just because there are players like that, doesn't mean the game should be changed to accommodate them if it comes at this price.
The fact is, even if the clock was changed, there would still be players who played faster then you, and didn't resign until your clock ran up, and you lose by time.
There's no way around people like that, but I find that there are more people playing honest Go than that.
Time, marking stones, I hate to say it, but in the end online Go is an honor game.