Here is a more radical way to do a tack

first off, communication in the boat is needed on when to tack/gybe.

Crew is handling the mainsheet all the way.

Helm: "Tacking in 3, 1 - 2 - 3 - Tacking." Starts the tack,
Crew: Sheets in to help the boat to head up.
Helm and crew heads towards the other side, mainsheet is slack.
Crew: On trapeze with main sheeted for acceleration. Crew is responsible for stability.
Helm: Moving into trapeze as it takes longer to flip the tiller behind the mainsheet.

With practice in low/medium wind conditions this can be a very fast way to tack. The key is to communicate and get in synch. A certain amount of trust in the ability of each others is mandatory with this method

Gybing from trapze can be done much the same way. Have the crew on trapeze until the tack have started. Then let crew come in with the sheet in hand (this eases the sheets) and just steer trough the gybe. Again, communication, sync and trust is needed, together with some structured training.