" I'm no expert, but my understanding is that hooking up pre-existing databases in this way is very, very hard."
no it's not. you stream out a common and documented data format and tell all those others to "here is your data, parse it and get it into your system.
You dictate the data and it's up to the other parties to deal with it. If anyone ever said, "we will meet their needs" they need to be beaten with a very large stick in the parking lot near the dumpsters until they die.
you define your data format and send it. ALL the insurance companies have staff on hand that would easily make interface logic to get their data in/out.