Well, there was no trick, except maybe using the original 37xx boot.bin for running update.txt, as the 34xx boot.bin crashes while being executed on 37xx (and "system software missing" is displayed immediately).
I was going to compare 14.bin to the flashed firmware and see if the flash chip doesn't corrupt the stored info.
And also I have a "hypothesis" that in most cases curing regions 41 and 48 (the internal filesystem) should be enough to cure a device. So I tried to erase those regions. Now you can try flashing back 41.bin backup to restore your device's model number.
Erasing region 91 was suggested by lolypop000, but this region doesn't exist apparently.
I have no idea why your device was unable to access the internal filesystem after formatting with RMPREPUSB. Probably it doesn't always format fine, depending on the previous filesystem contents, as Windows does.
Here is the update.log file
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