If you decide to go with the functional orthodontist I would fight like hell to get some of it covered by insurance (or get reimbursed from insurance). It may not work, but I would still try. Of all the people I've worked with I've had very little luck with this, but it still worked occasionally. What's interesting is that for the exact same appliance, I found one doctor who always gets my insurance to pick up the tab (consult, molds, appliance, appliance fittings), where with other doctors I've had to pay out of pocket for everything (health insurance for TMJ stuff, NOT dental insurance). Another thing to try, even if the doctor you work with doesn't work with insurance, is to submit to insurance after the fact. It can take forever to get the money back, and often times you get nothing back at all, but I would still try.
Good luck with everything. I hope you find something that helps.