No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
You can certainly contact the CA and offer a portion of the money in exchange for delete. It may not be as effective as pay in full, but it may work. You also might consider trying PFD one account at a time.
Are they all with the same CA?
You can contact the OC and see if they still own the debt. If they do ask about some type of financial aid.
If they have it and can write of the debt they would need to get the accounts back from the CA as no debt would be owed.
If they say it is too late for that ask them if they can have the CA return the debt to them (they would then have to delete) and you pay the OC directly.