Start by looking up the policy on insurance B - you may be able to file your claim directly with the insurance as out of network. Probably with reduced coverage - but it would be an improved situation. I would also clarify that the issue is the hospital isn't in network, as opposed to the claim was rejected. If the claim was rejected you want to know why - because it could easily be a wrong diagnosis code, or just missing paperwork.

Your biggest issue is that you're near being sent to collections. The most effective lobbying on your behalf starts early on - since they know you aren't going away for months (however long they have to wait to send it to collections). Still - the general rule applies when seeking help - take lots of notes, be persistent, always be polite and ask to escalate.

You could look up what Insurance B would have covered if they were in network - but that's abstract to the hospital. Instead, I would look up what Insurance A actually paid and push to have it written off to that amount.

If someone says "we wouldn't do that" - agree. "I know, which is why I'm so confused that it happened". or ask for clarification "Right, so why would I have been told that? Did this change recently?"

In the end - know the date you'll go to collections. If it's getting really close - I would consider the payment plan option since it's usually interest free.