Health insurance overlap due to qualifying life event confusion, costing $4,000 unnecessarily. Need advice.

Note: Cross post. Also posted at r/personalfinance.

I need some advice regarding my health insurance situation.

My wife and child are on my health insurance. My wife started a new job in a new city on August 1st. When I called my employer on that date to ask if this would qualify as a qualifying life event (QLE), they confirmed it did and requested that I email them the eligibility letter. They didn’t mention any additional requirements, and I didn’t think to ask, assuming they would provide all necessary information. Based on their guidance, my wife signed up for health insurance at her new job, including our child as a dependent.

Her job had a one-month enrollment period, and she completed her sign-up in the third week of August. We finally received the ID card in the first week of September. When I submitted the eligibility letter to my employer this week to remove them from my plan, I was informed that it was too late since the 31-day window had passed. I learned that I had only 31 days to initiate the QLE through their portal and submit the eligibility letter—none of which was mentioned during my initial conversation on August 1st.

I escalated the issue to a manager, but they said nothing could be done since the QLE was never initiated. I regret not being more proactive about understanding the requirements, as I expected my employer to guide me.

Now we have two health insurance policies: mine, covering myself, my wife, and child; and my wife’s, covering her and our child. This situation will cost us about $4,000 extra.

I have a few questions:

Is there any way I can still trigger the QLE and remove my wife and child from my insurance?

Are there any options I might not be aware of?

Is there a way to reduce my financial losses in this situation?

Thank you for any help you can provide!