Advice needed on medical billing/coverage

My medical insurer (California, Kaiser) said at sign-up that they have a variety of preventative medicine covered under copays only. This included scheduled pap smears, yearly check-ups, mammograms screenings every two years, etc.

Thing is, they’ve never scheduled my wife for one of these mammograms and when she brings it up, they send us to the hospital (rather than the in-house radiology department) and bill us for diagnostic, hospital fee, doctor fee (he’s not there, it was run by a single nurse), etc and it’s $2k, when our insurance lists it as a copay. We pay the copay and three months later we get the bill.

Last time this happened I fought over it for a year, including twice getting the bill rep on the phone, them agreeing it was codeed wrong, them changing it and saying we’re in the clear, then being told a week later the code appeal was rejected and we’r stuck with the bill.

They’ve now scheduled her again through the same reaosn, despite her pointing out (again) that she hasn’t had the screening on the schedule they suggest and want their patients on. They’ve looked at her chart for blood work or pap smears or flu shots and now Covid too and suggested she get annual things, but not for this service and they’ve once again sent her to the hospital for this diagnostic, we’re just waiting for the scheduling call.

How can we avoid this phantom bill? It’s quite frankly untter bullshit that I absolutely will be finally canceling our coverage over and will not be paying, but ideally I’d like her to be screened since they haven’t done it and I just want to know how to speak with the scheduler and the desk clerk at check-in to make sure they aren’t going to charge us 15x what they claim three months later. Or alternatively, how to effectively and efficiently appeal a bs charge should it come down to it. I’ve paid them $600 a month for five+ years at this point and they’ve never screened my wife how our policy says.

*Or, unrelated, does anyone know of a clinic that does screenings for just a copay and not over a grand? It looks like Planned Parenthood would bill Kaiser for it, and that may put us into this whole bs cycle all over again.