No, not tilt. You need to mount it lower on an extension pole. It looks to me as if you are having to project downward at an angle. That's a no no. In order for the auto zoom feature to work the center of the lens can be no higher than the top edge of the screen. [People who don't use that feature can indeed project from higher hence the manual's implication that it is OK to mount it up higher than that.] That is my understanding at least.
[Edited from previous version]
In A/V reproduction accuracy, there is no concept of "accounting for taste". We don't "pick" the level of bass any more than we get to pick the ending of a play. High fidelity is an unbiased, neutral, exact copy (or "reproduction") of the original source's tonal balance, timing, dynamics, etc..
I don't think I could possibly move it down any further, you almost hit your head on it as it is now. Maybe I could go down a half inch or something, but I wouldn't be able to lower it enough to have the lens right at the top of the screen. Too me the picture looks great and I don't notice any issues with it, it is just the one button to switch back and forth. So I am stuck with manually shifting then?
To invert the old line that "If you can't raise the bridge, lower the river!":
How about moving the screen up to meet the projector?
So I can't tilt the mount down and then shift the lens up??
If you tilt the projector the image won't be a perfect rectangle, so it won't fit the screen exactly (even if you use lens shift). But if you mount the projector directly over a seat, there's no way you can walk into it even if it's mounted lower. I can see how that would be a pain if it means moving it forwards or backwards from its current position, but it works for me in a basement with a low ceiling.
If you visualize the keystone that caps an arch at top center (also called the "capstone"), it's broader at the top than it is at the bottom. That's where the term "keystone" comes from. By keeping the film and lens vertical and parallel to the building, but moving the film up and down behind the lens, the building can be brought into view without introducing that distortion, which would make the top and bottom of the building different widths, and the sides no longer parallel.
That's what both the mechanical and electronic shifts are modeled on - you keep the imaging panels parallel to the screen while moving the image up and down or side to side behind the lens, avoiding the geometric "keystone" distortion that tilting the projector would introduce.
That's why you shouldn't tilt the projector.
End of pedantry (for now).