Petrushka, since you suggested a follow-up:
What I ended up doing was packing the smaller plants in 12x12x18 boxes, and the larger yucca in a pair of 20x20x20 boxes. I chose these dimensions based on what I measured I could fit in the car, as three 12" boxes would fit side by side in the back of my car's cargo area, and the 40" box sideways in the back seat. The draecana was actually three separate young draecana stems, so I chose the healthiest and straightest one that looked like it would fit in the box potted, and gave the other two away.
The pots were secured in place with crumbled packing paper, and since the yucca was going on the side, I also packed the lip of the pot with packing paper then taped a "lid" of paper over it to secure the soil tightly. This was very effective, and the box did end up fitting perfectly in the car, with the aid of a Rubbermaid bin to get it tipped up into place.
Two hours before the car carrier arrived, in the large box, I placed three 72-hour heat packs, and in each of the small boxes, I placed one. I taped them shut loosely, then placed heavy blankets (a down comforter on the smaller plants, a quilt and some sheets on the yucca) loosely over them with two more heat packs underneath each. The rationale here was that if the boxes outran their oxygen supply and quit reacting (a known issue with heat packs), the outer heat packs might at least keep producing an insulating warm layer under the blankets.
I was anxious about this since, when the day came, a 96-hour trip was projected due to weather, with the last night scheduled to be a winter storm. I was hoping for the best as it was too late to change plans..
Fortunately, the car carrier arrived in Arizona a day early, but still had to cross the Rocky Mountains in an overnight snowstorm with the lowest temperatures of the journey. When the car arrived, all heat packs were cold and hard. (Some heated back up after some time with the boxes open, which indicates to me that they did run out of oxygen and stopped reacting before they ran out of chemicals.) The boxes were cold and clammy to the touch, and the pots felt chilled.
However, as far as I can tell, no casualties. The croton, the plant I assumed I was likely to lose, has somehow not defoliated at all. In fact, it apparently loves Arizona and began producing new foliage from all but the tallest stem within a few days.
The one "victim" was the draecana, which I had had to repot at the last minute to remove its neighbors and situate it low enough in the pot to fit in the box. This was poor planning on my part. I believe the stress of this, combined with the cold shock, was pretty severe, and it has lost around 20 leaves. However, the top half, while a little off-color and ill-looking, is still full and seems like it's trying to hang in there and make a comeback. Since it is now alone and I needed to repot it to a normal depth in fresh mix anyway, I down-sized it into the croton's old 10" pot, and gave the croton some more space to thrive in the draecana's pot. The draecana is sitting on my desk for a while where it can get some nice bright window light.
TL;DR: This can definitely be done, if you absolutely must and the timing is aligned in your favor. Check the weather, measure boxes carefully, pack securely, and make sure you have plenty of heatpacks of the correct duration.
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