Unlike many other plants, palm trees really really cant tolerate being transplanted, especially when they are sick. Most of the time, when palm roots are damaged, the entire root will die back. That isnt a big deal in most healthy palms (some palms are finicky and it does bother them) but sick palms will not respond well.
If you really have to remove it, then I suggest putting it in a pot. Just make sure the pot isnt too large because if you want it to go back in the ground, you will have to wait for the palms roots to fill up the entire pot to keep damage as limited as possible.
Good luck, they are beautiful palms so I hope yours makes it!
-Alex

It's only been in the ground since August, so I'm hoping the original rootball is still pretty much what it was and hasn't spread out much. Thanks for the advice, I'm hoping it makes it, too!

OK, we dug out the palm this weekend, and despite putting it in a good loose soil that it should've loved, we found the roots really didn't stray too far, if at all, from the original root ball. Most new root growth was down at the base of the rootball and didn't travel horizontally as I had expected. Even so, there wasn't enough new growth to do damage when we moved it(fingers crossed). We put it in a 20 gallon pot (original pot was a squat 15 gal). I added a fistful of earthworms to the pot, watered with Superthrive, and located it in a shady area that is 100% protected from the wind. This tree was always hesitant to grow. The only growth spurts it consistently had occurred a day after watering it with heavily diluted Growmore Seaweed Extract (happened 5 out of 5 times). I don't think it was as healthy as the first Chambeyronia I purchased. I'd like to water it with the extract again to help with any shock, but am hesitant because I don't know if it would harm or help. Any advice?