Cash accounting with refund process

I am working for a public sector client that has a regulatory requirement to do cash accounting. As part of cash accounting, only transactions that lead to a cash flow effect should be recorded according to the cash accounting principle. We have currently configured the system with standard accrual as the primary ledger and cash accounting in the secondary ledger. As part of the solution we want to use the Receivables Refund process to refund customers either based on outstanding credit memos or due to overpayments (the customer has paid to much and should be reimbursed the outstanding amount). However,