"Please note that once a lead hits MQL he/she cannot go through the campaign again per our settings."
This is where the design error is and this is what you have to change, sorry for being blunt
In the era of digital interactions, the life of leads in the system is a cyclic by essence and it is absolutely key that it is possible to recycle leads to a previous stage. Linear processes are a design from the past, when at the end leads would either turn into an opportunity or be discarded (and would come back to the system through a form fill out later).
Also, the mere fact that you do not have this information about the leads or that the lead is not reachable is an indicator that they probably should not be MQL. Maybe you could add some filters to simply route them to a "pre MQL" qualification stage, from which they could be recycled.
Also, when you recycle a lead, you may want to consider having dedicated, different campaigns for these.