Tropica moves planted tanks around Europe all the time. The actual tank is the "weakest link", in terms of being capable of the stress - tbis is correct. The hardscape ( if any ) and soil/gravel buildup must be in such an arrangement, that they don't fall apart "on the road". Removing a small corner of gravel to empty more water is my trick, too. This stabilise all.
Plants will survive fine for at least 24 hours (probaply longer, but no promises) if carefully covered by thin plastic relatively tight around the plants. Even Amano and cherry shrimp survive happily on this environment.
The "flexible but firm" plate, to ride on (polystyrene is nice) is essential.
If possible, bring some of the "old" water along, since this is ofcourse quite a heavy waterchange 😉
Good luck - it's indeed do-able.........
Mick.