I think disputing the charges is a great idea!
Suggestions:
Find out the name of the Director of Billing Office at the hospital and the name of the Associate Administrator.
Write a letter to billing office director, cc AA
Ask for a copy of the UB-92 and a copy of the itemized statement.
Also request them to respond to your request to know what the hospital agrees to receive from the insurance carriers for those who have coverage for the same charges.
I think your idea about the actual statement your wife signed to accept these charges is really good.
Ask for a response within a certain time period.
I hope they drop the charges or at least negotiate to charge you only what is acceptable for insurance.

