I've moved with the Fantastic Furniture Detolf equivalents twice, and both times they remained assembled for the move and no breakage (and they were townhouses so up and down stairs). However that was with professional moving people.

If the shelf fits through the doors, might be worth calling around to see if they can handle it.

Re the TFs themselves - I've found the big plastic tubs you get from Bunnings are great, just put a layer of bubble wrap between each layer of figures (making sure to remove their weapons and straighten them out so they're not in weird poses). Haven't had any breakages or issues from moving.
Good luck!