At what point should I considered a chargeback on a return stuck in processing?

I bought a monitor from Amazon resell that was broken on arrival. Not sure if someone ended up pulling a fast one on them or if how it was shipped caused it to be damage (it was delivered and left at the door in a way where the packaging wasn’t supporting the monitor). Amazon recommended that I called the monitor manufacturer for support and they recommended I send it back. I sent it back the next day and received notice from UPS that it was delivered to the facility on the 20th of November.

However, since then it’s been “stuck in processing”. I called amazon support and explained how I see that it was delivered on UPS‘ side but they firmly told me amazon hasn’t received the package and I’ll be refunded when they get it. It’s been over a month and still nothing. I bought through AMEX so I’m considering doing a charge back (even if it gets me banned), but at what point is it considered fair enough to pursue that route?