How do you stop figures falling over on the drive to a show?

Hot glue is actually fine for this if you do it right. Run a thin bead around the base of each figure or tree, then once it's set you can pop them off later with a dental pick or a plastic spudger and most of the glue peels off the paint in one piece. The trick is a thin bead, not a blob. A fat lump of glue around the feet is what shows up at viewing distance. I've hot glued entire crowds down for transport and barely noticed it afterwards. If you're still nervous about the church or anything delicate, just take it off the module completly and carry it in a box. Nothing beats removal for the fragile stuff.

White glue under figures on a smooth surface never grips well because there's nothing to key into. That's probably why half of yours still lift. For rolling stock, box everything separately. Shoebox-sized plastic storage tubs with foam or scrunched packing paper work a treat, one layer of stock per tub with dividers if you can manage it. Anything that goes in a layer cake of foam over the whole board will find a way to bounce and scuff. Locomotives especially, wrap them in a bit of acid-free tissue first so the paint doesn't mark.

For the scenery on the board itself, a sheet of thin foam or even corrugated cardboard laid over the top, taped down at the edges but not touching any detail, will protect trees and buildings from knocks. Cut a few notches where tall things stick up so the sheet sits flat rather than pressing on them.

One more thing, take spare wheels, couplings, and a bottle of superglue to the show. Something always lets go on the day and you'll be glad of it.

I'd push back on the 'hot glue peels off clean' bit. In my experiance it grabs the paint on cast figures and takes a chunk of it with the blob, especially on anything with a matte finish. Tried it on some platform figures years back and ruined half a dozen. Poster putty under the feet works fine for car journeys, or just lift the delicate ones off and pack them like the other reply said. Only glue down stuff you'd be happy to lose paint on.

Poster putty gets my vote too. Used it on my old branchline module for figures, fences and a couple of small sheds and it all survived a bumpy trailer ride to two shows without a single casualty. One thing I learned the hard way though, don't leave the putty on for months afterwards. I forgot about a few blobs and when I finally peeled them off the paint had gone slightly greasy underneath and the colour was dulled. Now I take everything off as soon as I'm home and give the spots a wipe. For the bigger buildings I screw a thin wooden block inside them and drop a screw through the base of the layout into it, no glue involved at all.