Say hello to my little friend...
The conductive glue route worked beautifully, though it was definitely a trial to put all the delicate pieces together. Anyhow, here's what I did:
The glue I used is called "Surface Mount Component Fix" (I call it SMC glue here) made by a company called
Anders Products . Here's the action shot:

You actually need to pour off the top layer of solvent when you first use it, and then stir it back in until you get a good consistency (think Thanksgiving gravy thick). It can get a little messy, which is why it looks like I had 10 cups of coffee before opening the jar... well, I actually had 3 or 4 come to think of it.
Like it's sibling product, Wire Glue, it seems to use graphite for conduction. However, the resistance is much lower, at least in my testing. Since I ordered both products, I painted a line of each on paper, and measured resistance at 1mm distance (between probes) when they dried, The Wire glue was 3K ohms (!) and the SMC fix was 200 ohms. Wire Glue MAY have worked for this, but the SMC fix seems a safer option.
So I painted the LCD leads with the SMC fix, using a toothpick as a stylus. I actually whittled the end of the toothpick with an xacto blade to get a finer (0.5mm roughly) point. I also dipped an end of each wire in the glue and let that dry (about 15 minutes). Basically, I "tinned" the wires and pads, to use soldering terms. Then, I dipped the wires in the glue again and placed them on the LCD pads. I found tweezers to be useful here since the wire is 30 gauge and approx 1cm long and the pads are only 0.5mm apart. I actually did slip on one wire and wound up bridging two pads with the glue. Fortunately, it was easy to scrape a channel between the pads after the glue dried, using a fine-tipped xacto blade.
I let the SMC glue dry/cure for about 6 hours, and then added some 2-part quick drying epoxy on top to protect the connections. The SMC glue is pretty brittle and would not hold up on its own to any wire-bending stresses. I let that cure overnight.
Next, I trimmed the open wire ends to a reasonably even line and then soldered them to the LCD driver board. In the pic, the lcd screen is face down, and covering the NXT keypad contacts.
Next, I (carefully) bent the wires back, rotating/lifting the screen until is was visible. (Here's where the epoxy reinforcement is key.).
Time for a system check....
With the screen working, the last thing to do was to finish bending it into position, which is basically 180 degrees from where it started.

As you can see in the picture, the fit is pretty tight. The keypad needed a little finessing to get it seated under the wire.
That was basically it. The biggest pain in this fix was the wires - I went with solid-core because that's what I had in my supplies but I think if I did it over again, I'd try some stranded wires...maybe even some ribbon cable like that from an old IDE hard drive.
Now on to the important stuff... ROBOTS!!
