My solution to this conundrum is to anticipate the opposing straight driver's arrival, and match it. I.e. try to arrive at the intersection simultaneously and a beat later so we can then both go at the same time, with them continuing straight and me turning left behind them.

Or, I might get there a bit faster so It's crystal clear that I was first and I can get my turn over with while they're still coming to a stop.

But that gray area in between is no good, for the reason you say: people don't agree on the order of operations. Better to avoid it entirely.