In my experience changes to seats can be completed both online and at the kiosk even after the initial boarding process. And the options available online and at the kiosk are not identical so no harm in working both. And yes the individuals upgraded to first are often the individual with the exit row seats in coach so ironically the best seats are often available just prior to departure.

Requests for a seat change to accommodate a special situation such as the 6' 4" individual or the individual with a cast are often best addressed via the gate agent as seats can be put on hold by the gate agent. Otherwise the gate agent is often too busy to explore options for a better seat.