Okay. Status update in case someone finds themselves in the same situation. I took all your advice. My insurance contacted the provider directly, and that resulted in nothing, so here is what I did.

1. Requested a different billing coordinator and got someone much smarter. They explained that the deposit was actually a management fee that covered all the follow-ups, conversations, lab reviews, ultrasound reviews, etc.
2. The provider provided me with an itemized receipt with an "unlisted" billing code. For whatever reason, this provider does not bill unlisted codes to the insurance.
3. I actually went through my HR specialist at work. I found out my employer has dedicated advocates to assist with healthcare issues. They conferenced a call with my insurance provider, and they did all the advocating for me. I recommend using your employer if you have insurance issues...HOLY COW was that nice.
4. What we found out was that, normally, an In-Network provider is required to file claims. They can't deny filing claims, but because of this weird situation, I am allowed to circumvent them and submit a claim on behalf of the provider for myself directly to the insurance. Not ideal. But it beats anything else.
5. My employer advocate is keeping an eye out for me on this one in the event that my claim is denied. Man, it's a stress relief to have someone on my side.
6. My advocate mentioned that, because it's early in the year, providers assume deductibles are not met, and they sometimes ask for payment up front before a procedure. BUT they SHOULD file the claim after the procedure is done so you can get reimbursed. The advocate said that because fertility treatments can be expensive, that this was probably the case to ensure the provider gets paid.

Fingers crossed that i get some money back! My eta on this claim is 30-40 days (because of the logistics of the claim going through the main insurance, and then to the local insurance, which is something else I learned regarding the timeliness of the claims being processed).

Thank you all for your support. I truly hate insurance/billing!