How would you correlate the number of color spaces with the exactness of the image alignment, and same question for smoothing parameter?
More color spaces lead to a more exact match. A lower smoothing parameter does the same.
Sounds like a higher smoothing parameter is better when the sources aren’t pixel-perfect. Is a higher number of color spaces always preferable, with the only downside being time?
Yes, this is true.
Also, would it make any sense at all to create a collage of multiple frames (twice, per source) and feed that into the tool for a more informed LUT to export?
Yes, but use plenty of color spaces (>20) and set the smoothing factor to about 0.1.