>>5
The negation of "Kagami is more beautiful than Tsukasa" isn't "Kagami is not as beautiful as Tsukasa",
because even when the former sentence is the case, Kagami and Tsuakasa can be equally beautiful.
But your latter sentence is negating this possibility.

>but I find that the former interpretation is far more likely. I can't explain why.

I can't explain clearly either, but ほう plus the が particle puts heavy emphasis on the immediately
preceding word and tends to make the following predicate be interpreted directly with the emphasized
word as one big chunk.

Anyway, to avoid this unwanted ambiguity, the negation of the former sentence, "It's not the case
that Kagami is more beautiful than Tsukasa" or, more simply expressed in English, "Kagami isn't
more beautiful than Tsukasa", can be expressed as follows in Japanese.
かがみよりつかさの方がきれいというわけじゃないです。
The extra phrase というわけ is inserted to make the preceding phrase be interpreted as one big chunk
and the follownig negation negates this big chunk. There can be other phrases that does the same thing
as というわけ. They are kind of functinal phrases if you will, not so much as semantics or
pragmatics-laden phrases.