Can I convert the local to master and still continue to terminate AP's to it?
It depends how your APs discovering the controller .
For this case you are probably better off doing DHCP option 43 and based on the segment/VLAN if these are unique to each location and point the APs to the right controller
Since these 4 locals are scattered around the country, I'm guessing that I will lose connectivity to them when hte master-local GRE tunnel goes down. Is there any way to do this procedure where I can maintain connectivity?
Once you make the change from Local to Master the controller needs to be rebooted , these keep the same IPs and routing doesn't change you should still be able to reach them
Each local is currently properly licensed for it's own AP's. Will this new design impact licensing? Keep in mind we are running older code that doesn't support the new centralized licensing feature.
If those are properly licensed and you are not planning on adding more APs that the supported license count you don't have to worry about having centralize licensing or loosing any licensing capabilities.
Lastly, other than just ease of configuration, is there really any benefit to using a master-local design when I could just convert them all to standalone masters?
The advantage of having the Master-Local is that it allows you to have a single point of configuration and every controller has the same config.
Once each controller becomes a master you will loose that , which means that each controller will have its own config.
The caveat to that is I NEED to have point-to-point tunnels of some sort to allow connectivity between them. Thoughts?
Don't quite understand this question , can you give a little bit more details?
Do you currently have any type of AP redudancy configured ? in case of failover scenario ?