@e-bits, firmware and instructions are posted at https://github.com/TheThingsProducts/gateway/tree/master/firmware.
I just ran through the firmware updating procedure, but unfortunately it didn’t make any difference for me. Not sure what to try next as I’m not getting any UART output nor signs of life…
UPDATE:
My gateway is alive again! 
It turned out I had a badly formatted micro SD card; I originally formatted it on a Windows 10 box as FAT32, but the gateway only picked it up after I formatted the card as MS-DOS on MacOS.
Anyway, after inserting the card and turning the power back on, the gateway picked up the new firmware in the update directory and lit up like a Christmas tree! After a while the ethernet link is active and the SSID is also broadcast. Currently the gateway is registered, activated and online. Oh joy!
The UART is also transmitting now and I can monitor it.
Thanks to @milanoengineering and @mrjdomingus for helping out!
Thanks to @htdvisser for https://github.com/TheThingsProducts/gateway.