The fish do need the bacteria from the old tank, else the new tank will begin a new cycle. Transferring over the filter will be a big help -- transferring some gravel would help, too. Moving over some of the tank water might reduce the fishes' stress, but it is not critical. The tank water is the least important part of this equation.
No need to wait after you transfer the gravel and filter over, and get the filter running. If you use a water conditioner (Tetra Aquasafe is good, I use Jungle Start Right -- it doesn't matter as long as it takes care of chlorine AND chloramine), the dechlorination happens very quickly -- for our intents and purposes, instantly. You do not need a bubble wand to dechlorinate when a water conditioner is used.
To sum up, here's what I would do:
1. Transfer gravel over from old tank.
2. Partially fill new tank with treated tap water.
3. Transfer filter from old tank, get it running.
4. Top off new tank with old tank water.
5. Transfer fishes carefully (use a water bucket rather than a net if you can -- since you are transferring old tank water over anyway, this shouldn't be a problem).
Good luck -- do you mind if I ask why the extra 18 gallons are such an emergency?
Edit: To answer your second question, the Emperor 400 should be fine for a 55G, but it is always good to have extra filtration, so if the 280 is just sitting around, it wouldn't hurt to get it running alongside the 400.