Switching the balances around likely won't do much, if at all. You will very see a ding due to the new account reporting and possibly due to any drop in AAoA. IME, new accounts cost 20-25 pts with most/all of the points returning within 6-12 months as the new account ding goes away.
If I had that, I'd throw extra money at the car balance then refi the home in December. If the balance is low enough (or paid off), then your lender will ignore the payments from DTI calcs if soon-to-be-paid off and that will look better for your credit (not score...score likely won't change even if paid off).
