I feel for you! The insurance company we used to have was terrible. Every claim that was submitted would either get denied (even if it was a covered visit) or would get "lost". I would receive a bill from the docs office saying that since my insurance didn't pay, it was my responsibility. Then I would have to call the insurance co, who usually asked the claim to be resubmitted, then call the docs office to have them resubmit. The average length for a claim to be paid was about 3 months.
In extreme cases it took almost a year for a claim to be paid. For my sons surgery last year there were so many different bills (the surgeon, the hospital, the anesthesiologist, the outpatient area, the lab, etc), and they all got paid at different times. It was crazy.
Many of the employees at my hubbys work complained about the company and when the contract came up for renewal the employers discontinued that insurance company. Even though our new insurance is more expensive, I'm glad we switched because I haven't had any problems with the new one.
Good luck with your paper work. And don't worry about any of them going unpaid, I know from experience that if someone doesn't get their money, you WILL hear from them!