After aligning the excitation beam, I was able to take some scans in the x- and y-directions with the new angle of incidence of the excitation beam today (Tuesday). As I mentioned already, this "new angle" was completely opposite of the initial incident angle. To better see this, I have attached a sketch below in which the initial incidence is shown by the red setup and the switched incidence is shown by the green setup. The stand was moved a little between the two setups, but only to gain extra length on the arm which went to the lens for focusing the excitation beam.
The black dotted line represents the incident excitation beam and the grey disc this beam is incident on represents the Si wafer, while the grey square represents the translational stage. This is a view from above the setup. The angles of the two beams were not perfectly equivalent, but by "eyeballing" it, the two were very similar (and the exact angle does not matter much, just that the angle is on the other side of the initial angle).
Since the orientation of the stage was not changed, there is nothing to correct for in the beam profiles along the x- and y-directions. The scans for this switched incidence are shown below along with the scan from the initial setup, which I took yesterday.
It is rather clear that these two different scans are almost identical in shape over the x- and y-directions (with the x-direction scan looking almost more similar to the initial incidence scan than the initial vs. switched in the y-direction). The y-direction still gives us a Gaussian and symmetric shape, but with a little skewness maybe in one direction as compared to the initial scan. However, we are most interested in testing the obvious skewness that has been showing up in all of the x-scans as an attempt to see if the incident beam angle was what caused the skewness -- but by looking at the plot of the two x-directional scans, it should be pretty clear that the angle of the incident excitation beam probably does not effect the skewness very much and there is something else that causes this skewness.
One idea (which is pretty simple) is just that there is a misalignment of the parabolic mirrors in the actual microscope design... which is, in theory, why such a profiling technique is useful -- to test the shape of the beam in order to be able to adjust it for the desired shape (probably Gaussian).