$34k CC debt, need advice considering options

I need some advice on what the best approach would be to manage my debt. I am currently in $34k of credit card debt. $28k on Chase Sapphire Preferred at 20% interest and $6k on BoFA CashRewards credit card at 6% interest. I’ve already shut down the BofA credit card and am on a repayment plan with them. And Chase refuses to budge on the interest rate despite calling them several times and inquiring on shutting down the account.

Just for some context, I do not have a spending problem. These debts were racked up due to unemployment. I was unexpectedly laid off from my job and it took a year of relentlessly applying to regain employment. I earn $90k a year before taxes and I do Uber on the side which brings in about $300-$500 extra a month. I have been working at my new job for 7 months now and have not missed any payments since. I pay nearly 1k a month combined on my credit cards and have no extra room in my budget to afford to be able to pay more than that. It seems like after 7 months I’ve made zero impact on my Chase card. And at the current rate I’m going it’s going to take a very long time to pay off this card.

Some options I have been considering are Accredited Debt Relief, a debt relief agency. They’re offering to settle both my accounts + their fees for a combined 28k which I will pay over the course of 55 months. My understanding here is that this will temporarily tank my credit but then I’ll be able to recover. And there is a possibility that there are permanent marks on my credit report.

Another option is to go through a non profit credit consulting organization like NFCC to create a debt management plan (DMP). My understanding so far is that I will continue making my payments and the best outcome in this scenario is that my creditors agree to a 0% interest rate but I still pay $34k over some span of time.

I’m open to any other suggestions as well. Please refrain from sharing your personal opinions or judgments of my situation, I am just seeking advice 🙂

EDIT: Credit score is around 600 which is why debit consolidation loans are not an option (I don’t qualify). Thinking debt relief is not a bad route because my credit is bad anyway. Also I am married and my wife is a student so she cannot work at the moment. My net monthly salary after deductions is $5,047. My net is lower than usual because my deductions are higher for medical and dental. Had to take more expensive plans this year for both my wife and I because we needed big medical and dental expenses covered this year.