Well, I managed to create a custom boarding pass with all the information I wanted to include using the Google Wallet API. (Unfortunately it's not really possible to get rid of the "[TEST ONLY]" in the header without requesting approval from Google though, so I'm not sure my tool is terribly useful.)

Still, it barely took me 1 hour of playing around with an unfamiliar API. BA just don't give a rat's arse about digital experience and tech in general.
Sometimes I'm tempted to quit my job and spend a year or so fixing all the digital services for every company with ...... IT that I'm forced to use as a customer. Something tells me that BA aren't looking for help in this department though, not even if you're willing to be badly underpaid...