I cannot find any resources that explain WHY chordal 7ths, when dealing with chord progressions & voice-leading, often resolve downwards. ... Is there a more generally agreed upon reason for this that I'm missing?
I think what you're missing may be that in traditional functional harmony, the seventh of any chord is virtually never the seventh degree of the scale. You never have a I7 or i7 chord because the seventh chord is dissonant -- unstable -- and requires resolution, whereas the tonic harmony requires stability. If there is a seventh chord built on the tonic scale degree, therefore, you analyze it in a secondary context, for example as V7/IV or IV7/V.
With this in mind, think about which scale degree the chordal seventh is likely to be.
Perhaps the most common seventh chord is the dominant seventh chord. The seventh of this chord is the fourth scale degree. The defining feature of this chord is the tendency of the diminished fifth to resolve inward by half step to a major third. In other words, the tendency of the chordal seventh to resolve downward is equivalent to the tendency of the fourth scale degree to resolve downward.
If the seventh chord in question is built on the second, fourth, or sixth scale degree (as is also common), then its seventh will be ^1, ^3, or ^5, so it won't resolve contrary to the melodic tendency rule in question, although it will be inconsistent with that rule to the extent that it will have a tendency to resolve whereas that rule suggests that it shouldn't.
This leaves the seventh chords built on the third and seventh scale degrees. As with the dominant seventh chord, the seventh of these chords is one of the tones that supposedly has a downward melodic tendency -- either ^2 or ^6 -- so again the two principles are consistent rather than contradictory.
Another way of looking at this is through the lens of voice leading, through the rules of counterpoint. There, a seventh is a dissonance that requires preparation and resolution. It is the inversion of a second. A second resolves outward to a third, not inward to a unison, and therefore the seventh resolves inward to a sixth rather than outward to an octave.