When your status only allows you a crack at a FC upgrade "at the gate", how do you avoid getting beat out by those who checked in ahead of you on a connecting flight?

I flew recently LAX-HOU-PBI. The airline said I could try for an upgrade "up to two hours" before my first flight. This was a companion airline, so although I had Gold (lvl 2) status on my native airline, I could only upgrade at the gate. Got to the counter exactly two hours before, and already all 22 FC seats were taken on the first leg. The reason: people who had originated somewhere else and were connecting at LAX had started their journeys much earlier, before I was allowed onto the upgrade field. In other words, I never had a shot at an upgrade on the first leg.

Is there a way around this problem?

I didn't mention the airline because I don't think this is specific to any one of them.