Is it actually possible to negotiate hospital bills after insurance?

I’m in Texas, if this matters. I need advice about the best way to approach hospital bills I can’t pay even though I am well-insured with an *expensive* BCBSTX PPO. I am sitting on about $4800 worth of overdue hospital bills from delivering my son back at the beginning of July. Everything looks correct based on the EOBs and the itemized bills I received (I disagree that 24 hours under a bilirubin light in our room should be billed as a Level 2 NICU stay worth $21,717, but the hospital reviewed it and says it’s appropriate so whatever).

I am waiting on the paperwork to apply for charity assistance as I’m flat broke and should qualify based on their stated income guidelines, but I’m wondering if it’s even worth filling out. When I asked about assistance with the anesthesiologist’s bill I was told they only offered a discount for uninsured patients. Do hospitals ever cut the amount due and just send an updated amount of my out-of-pocket spending to the insurance company? Do charity care policies take into account other savings or just income?

Also, my baby might need surgery now, so I’m wondering if I might as well pay the first hospital bill since he’s probably hitting his deductible this year anyway.

This sucks. Any help is appreciated.