[OR] Moved recently, botched ordering my specialty medication, am I screwed?

Heads up: in retrospect, I understand that this wasn't the smartest thing to do in the world. I'm very stressed, please don't try to make me feel stupid at this time LOL

I was living in Hawaii and recently moved to Oregon. In Hawaii, I had HMSA, but since moving, I switched to my local BCBS plan. I take a specialty, injectable medicine and had a prior authorization for it, and this usually costs me no money whatsoever. Before switching my insurance through my job, I made sure I got another order of my medication in.

A week later when I switched my insurance, I wasn't told my previous policy would be backdated-terminated to the date I actually moved, so I received my medicine and took it. However, because my insurance was back-dated terminated, and my previous insurance didn't respond to the claim until a few days ago, I'm getting charged out of pocket for this to the tune of about $4,000.

To avoid this, I did think about trying to get a PA through my new insurance and have this backdated, however my new insurance is contracted with a different specialty pharmacy. Does anyone know if it's possible to get my insurance company to make a one-time exception for this? I understand insurance companies are the devil, and this is extremely unlikely, but if anyone's heard of this being done please let me know 😭

If I can't do the above, does it just sound like I'm screwed? I really don't want to pay this at all since I normally get this medication for free, but let me know what you think