After giving it some more thought, and considering all the wonderful options you all suggested, we have settled (so far) on a rich brown with purple undertones- BM's Rural Earth 1239. The purple (suggested by several readers) was a great idea, as it turns the peach and green into a variation of a secondary color scheme (orange/green/purple)
I swear, I must have tried out practically every color in the fan deck. I didn't want to add any more activity to an already colorfully-overloaded space, so finding something to neutralize the peach that didn't clash with that mint was really hard. Reader Kelly mentioned it felt bottom- heavy, and I think that is really true. All that activity down below, with nothing to balance it above.

Thanks SO MUCH for all your wonderful help- I really appreciate it!