Turns out the hospital where my son was born is out of network, help!

Been on the phone about this one all day.

When I was choosing a health insurance plan through my new workplace I searched all of our providers to make sure they were covered. My wife goes to an OB office that wasn't listed on the "find care" tool as in network, but every doctor that works there was listed as in network (and it turns out they're in network) The hospital these OB's deliver at was not listed on the site at all, so I made the mistake of assuming that just like the OB's office, it was just the facility that wasn't listed, but since I checked all the providers we're good.

Now I'm on the hook for $30k that was denied. I'm trying to appeal with the insurance but as far as I understand it, this doesn't qualify for surprise billing because it's the inverse of what the surprise billing law covers (in network facility, out of network provider at the facility)

I'm planning to appeal with my insurance multiple times, I'm not extremely confident that this will work but was hoping someone could tell me otherwise. Any chances of my insurance paying part of this with multiple appeals? I don't have any out of network coverage with this plan.

My hospital has actually lowered the bill quite a bit so worst case scenario I can pay this by emptying out my HSA and digging everywhere else I've got. It's still a ton of money though so just want to explore all options.

This is my 4th child so you'd think I'd be better at this lol