one monthly payment to every debt collector at once

You can contact the local debt relief companies and apply for debt consolidation program. Once you enroll for the program, the consultant will negotiate with your creditors/collection agencies and will try to reduce the interest rates on your debts so that you'll have to make a lower monthly payment. You, on the other hand, will have to send a monthly payment to the debt relief company who will in turn distribute it amongst your creditors/collection agencies. Thus, in place of multiple bills, you'll have to make a single monthly payment.

Please be VERY careful when searching for any type of debt relief company, there is a lot of bad press about them lately from state officials, I have read several gov sites that are placing cease and refrain orders on various "debt relief" companies. Just choose wisely and do your research! Make sure they have all the required qualifications and licensing.