I'm going to keep refusing even if it means getting fired. I have not been getting any extra compensation from the carrier company or my company for doing their job, which I have proven to my boss is on their end.

You go with that. Let us know how it works out.

grab my phone and ask her to repeat the reason into the mic because I want anyone like HR or a lawyer to know what is going on...

Here's the deal. You can be asked to take on additional duties. It's in every job description ever created. If you want more money? quit! That's cool

I'm pretty confident this should just be a fantasy and I shouldn't act on it.

LOL. At on it. Tell someone. Report her to the DOL and see what they say (Don't do that. No one is asking you to do anything other than your job)

am I reasonable in refusing to do work for a completely different company when the upcoming shit hits the foreseeable fan?

Do you want to have a job? This is how your keep a client and how you keep your job. This is the definition of job security. This is how you keep a client happy by doing nonsense tasks you bill them for.

I've already proven to her that it's not an issue on my end and that carrier company is failing to do their job.

Do you want a medal? or a trophy? You just Identified ways to bill the client. You can work and charge them more money. Did you miss that step? Do you not want the kuddos?

You look at this as extra work when the company says "cha-ching" we can bill the client more. And you're wanting to argue?

Why not give it a week or two and see what happens?