You can easily convert Contracts/Renewals into a month to month contract at the end of their term by checking the "Renew as Month to Month" box on the synced Quote.
Upon "Booking" and Opportunity and when the future Renewal is created, this contract will turn into a month to month contract and the next renewal term will be 1 month. It will override any values you have set at the Contract level, such as "Match Previous" or "Annual".