pay sudden large credit cards using consolidation debt vs. mutual funds?

Thank you all very much for your analysis, and it is a privilege and a pleasure to read your work in this subreddit. I hope this is not too verbose, but just enough.

I’m considering shopping for consolidation loans or cards to reduce unusually high credit card interest vs. paying some from my mutual fund investments. I got a “preapproval” loan offer, for whatever it’s worth, from Prosper for $35,000 at an unknown rate and I don’t know anything about what’s out there. I don’t know what I can get with a 614 score and 72% utilization, but please let me know where to try. I guess I can look at creditkarma and bankrate. I was considering applying for one or two of those, just to say I tried it before considering my mutual funds.

My total debt is $16,560 out of a possible $23,100, 72% utilization, costing about $200/mo in interest. My February 2016 Transunion credit score is 614 of 800 and Equifax credit score is 613 of 800, having dropped due to high utilization for medical surprises since summer 2015. I will submit an Equifax dispute against three old delinquent credit card payments where I’d misunderstood the minimum amount by $10/mo while auto-paying. I’ve already removed some.

Income is at least $2300/mo with no savings anymore, but I'm selling stuff. Fixed base living expenses are fairly optimized at $1100/mo plus ongoing medical expenses of $700/mo and about $200/mo in interest, plus variable expenses like food, etc, so I'll be wiped for a few months yet to go. I still have ongoing medical expenses which I hope to end in the next few months, so I’m only paying the minimum on debt lately.

I have $50,000 in Oppenheimer mutual funds, about to be reconfigured to a moderate risk at a projected 6% APY, give or take, lol, auto-reinvested into itself. I have always kept Oppenheimer separate from my cashflow and debt, to protect it from such volatility (or my lack of confidence), but I can reconsider using it to pay some debt. I just wasn’t thinking of it as simply as just comparing interest rates, but rather as two firewalled worlds. I can withdraw at any time via mailed check on a week’s turnaround, and I have withdrawn $2000 now to pay my Sears card. I didn’t want to risk treating the investment goal as another debt to pay back if I was to use it to pay off credit cards, but I should eventually pay into the fund it monthly when debt-free.

I normally am totally debt-free every year or two, for about half a year at a time, other than Christmases and then summer 2015’s major medical expenses which I still carry. For example, most recently in April 2015, before the medical stuff, I was debt-free with $6000 in savings and an all time high 725 of 800 credit score. I had been using my Sears credit card with a non-revolving balance only for the purpose of churning reward points. I presently have a $750-1000 Sears or Kmart gift card waiting.

• Capital One platinum card

$6325 of $6500 at 20%

• Visa card

$1990 of $2000 at 0-10%

Balance transfer card, 0% for 6 months, then 10%. It’s with my credit union and I would have to reapply to try for a potentially higher but unknown amount.

• Sears Citibank Mastercard

$3259 of $6000 at 22%

• Carecredit

$2486 at 0%, to be paid off in 12 months

$1688 at 0%, to be paid off in 12 months

• Target redcard

$812 of $1500 at 23.15%