Couple of thoughts...
First of all, thanks for an interesting article and exploration. Some years back, I rescued an Osborne 1 from "Curbside Discount" along with a bunch of software. Apart from a burnt out bulb in the power button, it worked quite well. I certainly did not go as far as you did in taking it apart, mainly out of fear of breaking it.
If you can find a copy of Peter A. McWilliams' Personal Computer In Business book, it will be an interesting trip down memory lane...and I thoroughly enjoyed reading it. Mr. McWilliams was none too fond of the Osborne 1 and made that perfectly clear. He felt the screen was too small, the fan too loud (of which more later) and the character font unclear. His description of the screen's phosphor color was also not to be missed--"several shades of orange, not unlike a punk rocker's hair" IIRC. He also disagreed with Adam Osborne about screen size--Peter's thought being that bigger screens were the way of the future while Adam insisted that smaller screens would be all you'd see. In their own ways, I think both men were right.
(If anyone out there still has the supplement to this book that is mentioned at the back--I'd love to know about it. Likewise, I think there was a much later version published in the 1990s that I can't seem to find now.)
I was surprised to see that your system had what appeared to be a green phosphor display, and found the lack of a cooling fan interesting as well. Every O1 I ever saw had the cooling fan underneath a sliding door in the handle. I don't think there was a black and white version of the display--I definitely did not expect to see a green one!
As for the display, it's probably fixable. You should turn down the brightness and contrast dials before the screen gets a permanent line or a "belly button" burned into it. I would bet that the failure is either bad solder or dried up capacitors that have drifted far from specifications over the years. Bad solder could be determined by poking at the CRT board with a **well insulated** object. If you're not comfortable around very high voltage electronics, see if you can get a knowledgeable friend to help--and maybe you could owe them a favor or buy them dinner?
Anyway...that's a pretty cool walkthrough of the system. Thanks again for doing it and sharing the result.