Surprisingly enough, I got an (exceptionally polite and capable) agent after only 25 mins on the line. Unfortunately, upfaring without a change fee is not an option, but even with the change fee the whole itinerary cost 1200€ to upgrade, which I took because 1500€ return in J across the pond on the A330neo in both directions is still a great deal, especially with the Polaris lounge at EWR open again.
The only problem is that the conversation took place more than an hour ago, and I still have neither the charge to my credit card nor the e-mail with the reissued ticket, even though it was supposed to arrive "in a few minutes"

They had to TAP it at the very end.