Speedy procedure #5: If you have the chance, take a standoff parking position rather than an aerobridge. Then your engine start / taxi out will be independent of tug availability. If you are at an aerobridge, there may be a chance to pushback to a position where you can remain ready for no delay startup & taxi.
Speedy procedure #6: Make APU start rather than external air supply.
Speedy procedure #7: Start APU & close doors when pax, baggage & freight on board.
Speedy procedure #8: Listen to slot time extension requests. If you are fully ready, call advising immediate readiness for startup. You might get the missed slot.
Speedy procedure #9: Be prepared to taxi a bit faster if needed.
Speedy procedure #10: If the controller goes out on a limb for you, don't let him/her down. Other pilots in your company also need to be mindfull of this. If your company has a reputation for bending the readiness truth, or not making take-off time or en-route time constaints, don't expect too much co-operation from controllers. Don't forget the human element.