The Taller Girls of the Two Girls [Ellipsis]

Part of this, the part about what can be omitted, is definitely an English grammar question. You can omit either or both of the nouns in this construct. So all of these are grammatical:

the taller girl of the two

the taller of the two girls

the taller of the two (NOTE: This one is grammatical only if the girls are a salient topic, meaning they have already been mentioned earlier in the sentence or paragraph.)

The rest is more of a linguistics question, but in most X-bar theories (ones that refer to Phrases with Heads), all of these structures would omit the head rather than promoting "taller" or "two" to be the heads of their phrases. In some frameworks, this may not be the case. One big topic in syntax today involves proposing alternatives to and derivatives of X-bar theories and arguing for why those alternatives may be better. For this reason there can't be an accepted, universal answer to the question of phrase heads and promotion because there's no one perfect theory that we can use to answer the question. It's possible that X-bar is wrong and "taller" and/or "two" do get promoted, or it's possible that phrases and heads aren't optimal strategies for syntactic analysis, but it's outside the scope of this question and this forum to analyze this any further.