The thing I try, as strictly a trial, is to eliminate any pre-board announcement. If you are in a wheelchair, or standing there with two kids in your arms, the gate agent should discreetly scan your boarding pass and invite you to board without making an announcement.

It is the announcement itself that starts the rush toward the gate.

I have always wondered about a silent boarding process. No PA announcements until the last zone. Put a screen above the boarding pass scanner that displays, "Now boarding First Class. First Class only" without a word being uttered. Then, "SkyPriority and First Class may board now." And so forth. In my mind, the chaos begins the minute the PA announcement about pre-boarding for "those needing extra time" starts.