You are not facing an uncommon problem. I commend you on actually doing your maintenance on your projector. I just visited a very large scale installation where racks of amplifiers hadn’t been cleaned in nearly 6 years, and it really takes a toll on the equipment.
As for your question
I assume that the image is not square to the frame in that it is tilted left or right. Use the “pattern” button on your Epson remote to display a test pattern. Use your laser level to shoot a line across the screen, (have someone hold it level or use two nails once it is in position to support it) and line the level up with one of the pattern lines.
You can adjust the projector’s roll left or right to align the projector with the test line, this is done on the mount itself typically with a small adjustment knob.
If the front of the projector lens is not parallel with the screen, you will get a trapezoidal pattern left to right. See page 58 of your manual. Square up the projector to the screen meaning you need to adjust the yaw of the projector, twisting it left or right (as opposed to rolling it). Your pattern will again appear square and line up with the level line when parallel. This again needs to be done at the mount. Then use the horizonatl lens shift knob to move the lens left or right to center the image.
If the image is not squared top to bottom, you have a trapezoid in the vertical orientation, that is fixed by making sure the projector is level front to back (pitch adjustment) and the centering the image with the vertical lens shift knob. See page 58 of your manual. Some projectors do this digitally through keystoning, however this particular one does it mechanically with the lens shift knob.
I hope that this helps!
Let us know how it goes.