Since it was only two of us in the playoff, we chose the coin flip option after calling the TD (he was at the other course of the event) and getting it OK'ed. IIRC he did say we were going to be allowed to choose who went first (winner of coin[disc] toss). That being said it was immaterial, since I won and wanted to go first on hole #1. If that's not technically correct, I'm looking for correction on THIS scenario -- not ones other than this.
The way I read the rule is same as others—coin flip to see who goes first. Not who chooses the order.