I would take the hang up and try again approach, hopefully getting someone who knows what they're talking about.

As a point of reference, this very morning I upgraded an LHR-TXL flight, that was paid for on my company credit card, to CE (I know it's a short flight, but could use the TP's) using my personal one. As I have done on many flights before.

It 100% does not need to be the same card