Advice: Birth – newborn "out-of-network" but mother "in-network" (big bill ensues)

Looking for any insight/ideas/suggestions:

Colorado – baby born 9/14/24. normal birth, no issues.

When I ask, the hospital tells us to not worry about the baby’s birth bills since “mother’s insurance covers everything for herself + baby for first month/30/31 days. Don’t worry about that hospital stay. You can figure out the later visits, etc. once you’re at home.”

I then setup my insurance with my newborn on my insurance. Our newborn is currently on my plan, not my wife’s. More affordable monthly payments.

Yesterday I get a message from my new insurance company with an explanation of benefits indicating $12k + owed to the hospital because our newborn was not covered by wife’s insurance. The hospital we went to is out-of-network for my new plan, so my insurance will not pay anything for our newborn’s hospital stay, nor will the $12k go towards deductible, etc. It essentially is ignored by my insurance because it is out of network. We made the mistake of thinking that first month was with my wife’s insurance. Wrong.

My struggle/issue/annoyance: As new parents, we were in the dark. The hospital reps repeatedly told us to not worry about the hospital stay itself for mom or baby. We assumed they were correct, and I did not know what my future insurance plan for our newborn would be at the time. Because of their advice, I now have the full hospital bill for newborn (not mom – she’s backed by her insurance but still had to meet her high out-of-pocket max). Birth will end up being all of mom’s out of pocket, plus her monthly premium payments, plus mine $12k. (I get why people aren’t having kids.)

I assume I am screwed here, and I regret listening to the hospital representatives. Was focused on our newborn. I was naive, obviously. I didn’t really know who to ask, but it clearly shouldn’t have been the hospital.

Is there anything that can be done? Or does anyone have any suggestions? (Please, as I am struggling with this already, hold back the insults/”you should know better,”  “do your research first,” etc.) Thank you for any input.