I know you said you're looking for a solution that you can manage yourself, but wanted to provide you an option that I think will help reduce your hospital's risk as well as save you and your department time!
MyCOI tracking services truly help reduce risk. They're a team of insurance professionals who are experts in dealing with all of the details that come with insurance and certificate of insurance tracking. I can personally attest to their due diligence in taking care of their clients.
They help companies and organizations like your hospital reduce risk by going straight to your third party's insurance agents for these matters rather than trying to deal with your vendors.
myCOI's software and tracking system also delivers real-time results and work to resolve all of your non-compliant matters for your company.
They save you time by taking on all of your certs, feeding them into their system, and managing and monitoring them until they see results. They also do more than any other company or cert-tracking system out there to chase down non-compliant matters.
You can check out myCOI here:
http://www.mycoitracking.com/and contact them here:
http://www.mycoitracking.com/contact-us