I think restraining it would be difficult and paint would be a better option, but with such a large vaulted white ceiling you should look at a dark paint to add weight to the wainscot.

*re-staining. Autocorrect, sorry.

Hubby wants white paint, you want dark chocolate stain. How about a compromise with dark chocolate paint?

I agree, I would prime and paint the trim. Re-staining is very labor intensive.

Do you have this same stained wood throughout your house? If so, I would not change the wood trim in this room. Personally, I prefer stained wood over painted wood, especially in a house in a wooded setting. As for using a dark chocolate stain, I think it will make the room too dark. The wood does not appear orange in the photos. Depending on how the wood is sealed, you may be able to darken it slightly with a light rub of a mid-tone stain.