Modified the dongle - after cutting away the shell. Simply shorted pin 17 of the HDMI connector to shell ground - works.
And end result:
For now, I've left everything "bare". I kept a bit more wire in the short so I could add a switch, if I wanted. These circuit traces are very tiny, and I didn't want to have to go through the pain yet again of trying to solder a wire on those small traces. The Lapdock I got was one of those new-in-box (mine was completely sealed) English/Hebrew keyboard units. The Hebrew letters are small and in the lower right corner, and really aren't terribly noticeable. At least to me. I'm a touch typist anyway, so no big deal. Keyboard and mouse work. As you can see - Xwindows works too.d
Not sure how I'll finish it off. Could encase it in epoxy or JB weld - something like that. I may combine both the HDMI and micro USB together into one cohesive unit to give a bit more support to each other, and possibly shape the epoxy (or whatever) to the curve of the tray where the Atrix would normally sit. That way it would put less pressure on the connectors, etc.
So - it works, and I haven't "butchered" the Lapdock - my main goal at this point. I may well do that in the future, but for now I wanted something that worked without modifying everything. "Butchering" a $2 HDMI connector was no big deal, and I've still got a spare connector.