How do I directly submit a bill/claim to be processed by insurance (NOT for reimbursement)

Hi! I am a 38F in Illinois, estimated gross income before taxes for my household is $230,000.

Background info: I have two insurance plans. My primary is an HMO (BCBS IL). My secondary, through my husband’s employer, is a PPO (also BCBS IL).

I recently was seen at a reproductive immunologist. I knew going into this that they did not accept HMO plans of any kind, however they DO accept my PPO plan and are considered in-network with my PPO. Prior to my first appointment, I also took the extra step of calling BCBS PPO and gave them every single CPT code that this clinic gave me, to ensure that the services they provide are covered by the PPO plan (they are covered).
My understanding is that in this type of situation, in order to get the PPO to kick in and cover the claims, I first need to get my HMO to deny the claims (since they do not cover any of it, and they are my primary plan). The issue, though, is that the clinic claims they cannot (or will not) bill HMO under any circumstances, even in this case for what is essentially a formality. So when I went in, I just gave them my PPO plan info and didn’t mention my HMO plan at all. Problem is, it was submitted to PPO and PPO paid the claims as though they were the primary plan, which they are not, so presumably they will now ask me to pay. But I should not have to pay, because I already hit my OOP max on my PPO plan and this visit should be covered now at 100%.

But since the clinic will not submit the claims to my HMO plan, I need to do it myself. This is my question: How do I submit the claims to my HMO so that I can get denied, and then move onto submitting to my PPO? Please note that I am *not* asking how to submit a claim so that I can be reimbursed; I am asking how to submit the claim for processing *directly* to BCBS IL HMO.

Thanks for any help you can provide!!!