I am in a similar position. My wife and I have decent credit and high balances. We have been very diligent with timely payments, but we she fell ill this year, she was out of work for almost 4 months. I did everything I could to stop the bleeding, put the mortgage in forebearance, car note, etc, but between bills and her treatments, we racked up quite a bit of debt on top of what we already had. Currently we're at about 21k in credit debt between the two of us across 9 cards varying from 12.9% to 23.99%.
A credit union local to me worked up a magic concoction to really help us out.
We are refinancing our auto loan down from 9.79% to 4.4%, payment stays about the same, just now paying it off quicker. Not a big deal, but it helps in the longrun
They approved us for a 5 year personal loan at $16,500 to knock out a majority of our credit debt. The interest rate on this is 10.4%, which is high, but less than what we are paying, and the payment monthly will be about $115 less than the total minimum payment of the cards we are paying off.
They're also in the process of approving us for a Home Equity Line of Credit. Once we close on that we're going to pay the rest of the cards off and pay off as much of the personal loan we can. The HELOC is a 10year repayment at 4.0% interest, huge savings.
From there I plan to snowball Ramsey style.
Sorry for the long post but the point is that even though my goal was to try to go full HELOC, a good bank or credit union will really try to help you solve the problem.