Does the vehicle you drive have a heater? If so it may be slightly uncomfortable but wrap the styro in a thick blanket and blast the heat for a while, keeping the inside at the top temperature you care to deal with, it would be fine.
If you leave water in the tank the bacteria would be fine, but only just enough water to barely cover the bottom of the tank is fine, it will splash around in travel, keeping the gravel moist. I would not suggest leaving the gravel in the tank during travel, it will almost DEFINATELY scratch the glass (assuming the tank is glass) in the area the substrate is at, and if you were to shift or hit a large dip, bump, pot hole, etc it may shift enough to break the glass. Putting the gravel in buckets with just a little water would be fine, if you chose to do that.
You wouldn't have to re-cycle the tank, even if the bacteria died off, which I don't think it would, you could replace the filter media in your 55g tank and put that filter media in the new tank. The tank would be cycled rather quickly, and the fish could more than likely do just fine in that situation.
Best of luck on the 120!
