Firmware problem updating to High Sierra

Hello,

I have the following problem with trying to upgrade to High Sierra (10.13.2). Whenever I try to install, it fails with the notification that a problem with my firmware has occurred.

I have already gone through the solutions that I found on FAQ sites, which are SCM reset, NVRAM reset, hard drive repair and EFI and SCM firmware update. I have done everything except the EFI firmware update and that seems impossible to me, because the latest firmware that I can find is MBA51.00EF.B04 (2015-002) (on my Macbook there is MBA51.00EF.B02). Unfortunately, the firmware update is only for OS 10.9.5 and I have 10.12.6. Since I don't have a backup in my time machine with Mavericks anymore I don't see an opportunity to complete this last step and of course, I don't know if that would enable me to update to High Sierra, either.

Does anyone have an idea what I could do to somehow come closer to a solution?

Many thanks in advance!