It doesn't make sense to build an overlay network. That would cost billions and is wasteful. It is easy enough to create a tag for ER networks and give them the highest priority. If they came up with a standard versus try to build one, and then that way they can choose the vendor (meeting the ANSI standard), and have a backup if needed. LTE chipsets are good enough now to handle multiple frequencies.
The issue is that once this happens the piss poor tower DRP will need to be updated and some redundancy will need to be built in, not to mention extended backup power not unlike POTS USED to be.
The government rarely builds these networks anyways, they are always going to be built by a private company anyways, so why not just admit it and do it right..