Best practices for making missed payments outside of the current pay check date

I wanted to reach out to the community to get some feedback on the best practices as it related to off-cycle and on-cycle processing. Currently, our organization utilizes off-cycles only for reversals, not for positive checks, which are tied to our on-cycle checks for reporting. We have found a need to calculate missed payments faster than waiting every two weeks. What I am trying to understand is what are the reasons to do that as an off cycle calendar instead of an additional on cycle calendar. We are debating creating on cycle checks to process one off payments based on