Wife’s Employer fumbled FMLA, caused lapse in coverage

TLDR at bottom

I am mainly making this post to determine the best course of action following the described event.

My wife left on an FMLA leave for the birth of our child in February. Her employer contracted all of the FMLA paperwork to a 3rd party. On the day that her leave began, she made it very clear with her employer and the third party what her date of return was. The leave lasted 10 weeks and she provided regular updates to her employer regarding her return date. She also advised the 3rd party agency of her return date at least one other time during her leave (making two documented instances).

During the leave, as expected, we made payments to her health insurance company to continue coverage instead of the payments being automatically deducted.

When she returned to work from leave, her premiums were not deducted from her check, and we continued to receive bills to pay the premiums directly. At this point, my wife began to make calls to her company's HR and the 3rd party because it became obvious that her 'status in their system' had not been changed and was still showing her as on-leave. Over the course of the next 4 months, at least 35 documented phone calls (and several in-person conversations) were made by my wife trying to get this corrected. During the final month, we received a notice from her insurance company that her coverage was going to end due to her having been of leave for 6 or more months.

Just last week my wife's employer was able to finally confirm that they changed her "status" and that her deductions should continue as before. The problem is that due to their ineptitude, her coverage lapsed on the last day of the previous month. All claims that have been submitted for services rendered during the month of September to my wife and to my son (who happens to be extremely ill and has had 5 different claims submitted this month) are being denied.

I know that her employer is liable for the lapse in coverage, and I'm sure there's some blatant violation of the FMLA in there. My question is what is the most efficient way to move forward from here?
Do we need to begin making more calls to the unhelpful HR department, or would it be advisable to jump right into legal action?
Is this a situation where I could call the insurance company and obtain immediate reinstatement?

Any advice helps

TLDR: Extremely inept and negligent employer and horrendous 3rd party leave of absence contractor failed to notify insurance company of my wife's return from FMLA leave for over 6 months causing lapse in coverage. How do I go about getting reimbursement/reinstatement of benefits for claim approval during lapse period?