I won't pretend to be a functional expert in logistics or finance, but it seems to me that this is likely a configuration and/or business process issue and not a security issue. I'm pretty sure it is not common for organizations to take away access to MIGO entirely during month-end close. I think rather that most organizations will just do something like lock the period that is being closed, so new postings go to the new period. This should happen anyway, since closing is usually done after the period in question has expired.
You might have a look at Steps for opening and closing period – MM FI CO, but otherwise this question might be better raised at SAP ERP - Logistics Materials Management (SAP MM).
Regards,
Matt