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That's okay. I managed to fix it. It was NOT a software problem at all, though it seemed to be as inconsistent enough to be an issue. In a nutshell, this is what I was experiencing and what I did to fix the issue.
The screen was EXACTLY as the original poster described:
- gray bar (less than a half-inch thick) running about an inch above the bottom of the screen
- about two inches of black "dead space" on the right side of the screen
- an area of about 640x480px to work in
- under the gray bar the top portion of the screen repeated itself
It seemed to be an issue from a boot, reboot, or return from hibernation. If the screen appeared normally at startup, it did not malfunction as long as the computer was not shut down, restarted, or put into hibernation. It would continue to work fine from standby/sleep, however.
At some point, no matter how many times the computer was rebooted, the screen continued to malfunction. At this point, I decided to open the case and investigate.
The clip for the monitor on the motherboard seemed fine, but there was an awful lot of tape fastening various wires and lines into bundles. After I pulled the tape away (I imagine this, more than anything else, likely voids the warranty) to discover that the wires going into the monitor clip were BENT. I straightened them out, cleaned the connection, and reconnected it. After reassembly, everything worked fine. It has been two weeks of varied use, from ten minutes to check and respond to e-mails to hours spent researching or writing. I have left the computer in sleep and hibernation without issue and also shutdown and restarted the system dozens of times under varied CPU temperatures (thinking the heat of the unit had some role in the monitor's functionality - look at the routing of the heat sink assembly and you'll see why) and throughout the range of motion on the monitor hinges. Everything seems to be working fine.
Note that I disassembled the computer according to the instructions in the HP 1000 Technical Documentation, which is available in PDF for those seeking it. I also disconnected and reconnected the RTS battery for good measure and restored the BIOS to default/factory specs, all of which is detailed in the Technical Documentation PDF. Whatever element of my little computer's surgery that did the trick, I cannot say for sure, but if you're experiencing the same issue and don't want to go through HP's warranty work (again, my experience wasn't great, but only because of the extraneous circumstances in which I find myself), know that it could be something VERY simple.
Of course, follow all the precautions outlined in the documentation if you choose to void your warranty and attempt to fix it yourself. And it goes without saying that I can't accept responsibility for anything you do to your own computer. 
