Hi PhF,
I had earlier successfully updated from v1.1 (non beta) to the various v1.2 betas without problem.
But I decided to replicate your steps to see if there is a problem going from old firmware directly to 2.58.
I started as you did with a previously created backup that was created "Create Backup" in ApplePi-Baker (yep, MacOS X). My original SD was dated Dec 19, 2018 and I had created the backup in January 2019. If your original backup is older, what I did may not be applicable.
As usual, I used Restore Backup in AppePi-Baker to restore a new SD.
After I let the ASIAIR completely finish booting with the new SD (the green LED in the Raspberry Pi fully quiescent), I connected to the ASIAIR access point from an iPad. I then launched ASIAIR v1.2 (4th beta) and got the message window from ASIAIR that New Firmware needs to be uploaded (message says "Update from 1.02 to 2.58. It will take about 2 minutes").
After clicking on the green Update text, the ASIAIR switched to showing a "Firmware transferring..." message window with a progress bar.
Interestingly, the bar sat at 99% for quite a while (perhaps between 15 to 30 seconds).
After about 2 and a half minutes from the time I clicked on "Update," the ASIAIR app finally told me that firmware update has finished. Checking the About window of ASIAIR shows Version 1.2 and Firmware 2.58.
So, it is indeed possible to jump from old firmware to the one in the current Beta firmware without going through any intermediate firmware.
If you did not see any of the steps that I saw, perhaps you can report to ZWO (wait for them to come back from the weekend :-) which step was missing.
It might be worth downloading a new disk image from the web and use it to restore an SD card. Probably a last resort kind of thing since it takes forever to download that 32 GB image file over the internet, plus you also need to copy your original license file over.
Good luck,
Chen