Thanks for the reply Big. I figured it out.
In the JVC's service menu, there is a "lens reset". What this apparently does is tell the JVC computer board where the physical motor position's central position is. You have to calibrate this manually. In order to calibrate this lens reset properly, I had to find a way to get the shifts to be exactly center, vertically and horizontally. These are the steps I did to fix it:
1) I ensured, as best as I could, that the projector was square on the screen.
2) I centered the image shift mechanism in the vertical axis. To do this, I setup my projector on a table top, measured the distance from the floor and marked this position on the screen. This will be used to find the vertical center point of the shift mechanism. Pull up a test pattern that has a cross hair at the center of the screen, or use a menu item for reference. Ensure that the center point of the image is the same height as that of the projector on the tabletop. For this technique to work, the table has to be tall enough so that the projector's center line is somewhere on the screen.
3) To ensure that my horizontal shift was centered, I shifted the image all the way to the right until the motors stopped, marked some indicator (say the word "MENU" or could be a test pattern cross hair) position on the screen, and then shifted the image all the way to the left, and marked that position on the screen. I measured the distances between the left and right marks and divided by 2 to find the center horizontal shift. I then shifted the image so that my reference (in the case "MENU") was on this centrally marked point.
Once it is centered as described above, I was able to "reset" the lens position so that the computer board was in sync with the motors. When I entered the JVC service menu, I navigated to "lens reset" and this apparently told the JVC board that the current position was the central position. And this is what I had ensured by following the steps above. Once I exited out of the service menu, I all of the sudden had my full range of shifting back and lo and behold, it is no longer on the ceiling.
I hope this helps someone else who might run into this problem.