First, this map looks amazing
I don't think the Arena itself is a problem, the issue (imo) is the gates. One possibility is to some description explaining it (either pictures or text), another is arrows (or smt similar) but that'd look ugly. I'm sure there's a elegant solution.
PS.
You're not the first to use this "coloring in players color" trick, other maps already have it. For example
https://www.warlight.net/Play?PreviewMap=11033 the territories color the words. However I've not seen one done as well as yours.