How can I better extract the hidden images in FEZ's soundtrack?
A few pointers to help you produce more detailed results:
First, you may want to read about a phenomenon called Pareidolia. By tweaking and tuning parameters, you may be simply creating results through coincidence.
There is no such thing as the spectogram.
There is such a thing as a spectogram.
I've looked at some of the results already found that have been posted online, but none actually talk about the specifics of the spectogram used. This makes those results hard to reproduce (outside of running the exact same program with default settings). Why?
Spectograms have many, many parameters. Some explanation below:

Windowing function
First, there is the windowing function, which is technically any function taken from a function space (this stuff gets very complicated). Typically it's taken to be continuous or at least semi-continuous (a finite number of discontinuities).
Theoretically, this kind of space is of the order aleph-3, although practically we're limited by the resolution of the computer, or, the total resolution is N floating-point values big. Typically these have a 53-bit mantissa and are between zero and one, so we're already looking at 53KB of parameters for a 1024 FFT size spectogram.
Window size
This is typically taken to be a multiple of the FFT size, usually W = N. Ideally, at least one full FFT size is inside the window size. Complicated mathematical expressions can identify the resolution of a spectogram, which depends on this parameter.
Window overlap
In order to improve time resolution somewhat, when using non-rectangular windows windows are usually chosen to overlap to reduce spectral leakage losses. High window overlap factors tend to smear out/deform the image. Typically chosen to be 0.5 with most standard windows as that satisfies COLA.
FFT size
Changing the FFT resolution can change the shape and image of the spectogram through rounding effects and also has an effect on the time-resolution capability of the spectogram. You could compare it to the Heisenberg principle: increasing the sample count improves frequency resolution, especially at low frequencies, but reduces time resolution.
Must be a power of two for the traditional FFT algorithm to run quickly enough.
Has an impact on the speed of the visualization. Older programs tend to run with lower FFT sizes to enable real-time visualizations on slower computers. FFTs scale with O(N log N). See here.
Sampling frequency
May not match the recording frequency, in which case the audio is resampled before analyzing. Iff so, then the resampling method used can also impact the result.
Base frequency
Typically not directly configurable (typically the user is asked to select min/max frequency shown in the resulting image), the base frequency of the FFT is equal to fs/N, or the sampling frequency
Filters, transformations, etc.
Post- and pre-processing is typically used to improve the output quality for visualizers. Typically done to remove noise, compression artifacts and the like, they can corrupt hidden images, which are often of very low volume and may be caught by a noise filter.
Image width in px
Finally, the chosen image width and, iff different from the size of the FFT output, the resize filter can make an image fuzzier in quality. Ideally the image width is equal to the FFT output, though, if this is too big, the FFT output is an integer multiple of the image width. Take care to convert the image if needed with an integer ratio as well to reduce artifacting, and to use a lossless format.