A true DMP will make regular, monthly payments. Whether or not they're on time is another story. Typically, the DMP will draft funds from your bank account on a specific day of the month and then disburse a day or two afterwards. Posting to your respective CCs can take between a day for most large issuers to over a week for a mom and pop card. You should be able to work with your card companies to change your due date so that it will work with your DMP.
I am in a DMP plan with my discover and Citi cards and have had nothing but a great experience. I sent you a PM with the link to my company.
You can end up with lates during the transition to your DMP based on yoru due dates, however, my card companies gave me leeway once they found out I was entering a plan and let me go two billing cycles without making a payment. I would suggest having enough cash on hand to make the minimum payments on time until the DMP starts drafting from your account.
As far as waiting for your job prospects, that depends. I would go ahead and call a counseling company and talk out your situation with a counselor and be brutally honest during this conversation. I was recently laid off and am inbetween jobs. My counselor gave me great advice on what to do should my funds run out before finding a new job.
I, personally, am in a DMP with BofA. I used the co that BofA recommended and it's been awesome. I just pif'd one account, so I'm two years ahead of the game. My signature loan was lowered to 13%, so I paid that off first.
My BofA cc was reduced to 4% interest. Do NOT miss any payments, your scores will tank. Most of the programs are FIVE years. Late Fees, etc are done away with.
I recently closed my Lowe's Account and they offered me 0% interest, payments of $50/monthly for 40 months. You CAN do this yourself.
DMP that I use charges about $30 up front, then $15/monthly.....negotiable. Send me a PM if you would like to explore this option.