If it makes you feel better, I moved very recently about the same distance as you are. We moved everyone in one go (even a gravid female) and everything went perfectly.

I would put everyone in snake bags and in tubs or insulated boxes. Get everything set up as quick as you can. That is a short move, they should be fine.

As for the eggs, 15 minutes out of the incubator shouldn't be too bad. Just keep them warm as best you can (maybe in a cooler with some warm water bottles). Have someone holding on to the box so they don't get jostled around too much.

Keep calm!