It was advised in a few posts to close your accounts instead of allowing the creditor to close it. If I close the account, wouldn't that nullify any actions to get the creditor to work with me such as allowing me to apply for the hardship program (if they have one)?
I was hoping to close and see if I could initiate a lower rate to allow me to pay debt down faster instead of going through a DMP.

It really doesn't make that much difference whether you close it or they do. I used to believe it was important - now I think that's a myth. Perhaps on a manual review, a credit analyst might ask you why they closed it, but otherwise, since everything is automated, that little detail is not really a factor in scoring or granting credit. Same with the "lost or stolen" notation.