How to cover previous carrier to drop erroneous policy?

I switched employers several months ago and my medical coverage through them (BCBS) should have dropped in April. For whatever reason, the insurer still shows my coverage as active. I’m notified them numerous times over the phone and via their patient portal that I should no longer be covered. Likewise, I’ve had the previous employer accomplish their notification now three times to tell BCBS that I’m no longer covered. The insurer still is providing coverage erroneously and denies having received the official notification from my former employer and as of present has noted that I’m informing them I should not be covered but claims they can’t do anything without hearing from the employer.

Perhaps the employer is sending documents to the wrong place, perhaps BCBS isn’t tracking things internally, but either way, this is out of my wheelhouse yet somehow I’m trying to connect these dots. I’ve got a couple of big concerns here since my family still needs medical coverage while this is going on. First, I don’t want it to appear that I’m trying to use insurance I’m not entitled to, since presumably at some point somebody’s going to realize the mistake. Second, although my family and I are telling medical providers to use ONLY our new insurance (the one we SHOULD have), some are showing double coverage and trying to bill both. We’ve reached out to offices that my wife has seen in the past and trying to have them correct billing from April to the present, but none of this is moving fast. I’ve also got the fear that somehow a charge slips through the cracks, the payment from the old provider gets pulled back, and then it appears as a medical debt.

So is there any way to compel the old, erroneous insurer to drop coverage from my end, even if they aren’t in receipt of notification from my previous employer?