Setting to automatically cancel one-time fee memberships if payment not received within given time period

We need an automated way to warn users who purchase a One-time price membership that payment is outstanding and then automatically cancel the membership after a set period of time that we can specify when setting up each membership type (or have one general setting for all fee-based memberships which is probably all that we need).  

Currently we have to chase the people for payment via email and then manually go in to cancel the membership if payment is not received, which is very annoying and time consuming for us.  If the membership payment could work similar to other fees (e.g. guest fees on bookings, payment for event signup etc.), where a reminder email is automatically sent after x hrs/days, and then the membership is canceled after a further x hrs/days, that would be great.  It would be best to have a separate setting than those other types of fees which we currently have canceling after 15 minutes.. but if the easiest thing is to make memberships cancel after the same duration, then we can live with that.  As part of this feature, we would love to be able to customize what the reminder email says, but we would settle for something generic that says payment is outstanding and that the membership will be canceled if payment is not received by xxx.