Make insurance companies conform to a standard (not just similar) claim processing form. Allow any licensed insurance company to process any claim from any other insurer or government agency, then settle on a nightly basis the same way we currently do with banking through the Federal Reserve system. Allow the company that processes the claim a per claim processing fee that is part of the settlement.
Put in similar incentives similar to the 'Check 21' system to encourage electronic filing and image transfers. Make it as secure as the Federal Reserve's current ACH/Check Clearing network.