Explain the use of "mouthful" in: I've always called myself "Henny" because it's less of a mouthful than "Henrietta."
I think it should be one of these because "mouthful" is a noun meaning "a word or phrase that is difficult to pronounce":
1. I've always called myself "Henny" because it's less than a mouthful of "Henrietta."
2. I've always called myself "Henny" because it's less than "Henrietta" of a mouthful.
3. I've always called myself "Henny" because it's less than "Henrietta," which is a mouthful.
First: You are sorting out idiom usage. Understand that figurative idioms also have literal meanings. Literal meaning describes a thing as it really is: e.g., "The wedding gift was a crystalline canopy" is a literal use of "crystalline canopy," while "The sky was a crystalline canopy" is a figurative use of the same phrase.
Mouthful may be used literally or figuratively. You may say "I have a mouthful of alfalfa spouts" to literally describe what you are eating or say "Asking for oscillococcinum is a mouthful" to figuratively express the difficulty of saying that word.
Second: You are sorting out the language of comparison. In English there are prescribed rules for the language of comparison. One example misuses the language of comparison. The phrase "less than Henrietta of a mouthful" breaks the usage rule, which is the pattern "Something is less than something of something." In particular, "it’s less than Henrietta of a mouthful" incorrectly adds the article a to the pattern with an incorrectly used preposition of. This phrase is unacceptable in English.
Third: You are sorting out use of the preposition of. When of is used following a proper noun, it is locative or possessive: it indicates a location or a possession. An example of locative of use is the phrase "Macbeth of Scotlad.” It means that Macbeth lives in the location Scotland. An example of possessive of is the phrase "Chaucer of writing fame." This indicates Chaucer as the possessor of writing fame.
You define the meaning of the figurative idiom "mouthful" correctly. Remember though, if used in the wrong phrasing, it ceases to be a figurative idiom and takes on the literal meaning of how much you have in your mouth: a mouthful. In, "I've always called myself "Henny" because it's less of a mouthful than "Henrietta," the idiom "mouthful" is in correct phrasing, which positions it as a figurative idiom.
Your suggestion that "this sentence is usually ordered like the following: “I've always called myself ‘Henny’ because it's less than a mouthful of ‘Henrietta,’” is an incorrect suggestion. The phrase "is less than a mouthful" uses mouthful in its literal meaning because it fits the pattern of literal comparison: Something is less than something else: mouthful is no longer a figurative idiom in this sentence. The sentence now means that ‘Henny’ has a quantitative measurement that is less than what a literal mouthful of a person called Henrietta is. So the rearrangement of the phrasing from "less of a mouthful than" to "less than a mouthful of" has rendered the sentence illogical and absurd. Certain patterns of English words must be honored or the intended meaning is lost.
Finally, "I've always called myself 'Henny' because it's less than 'Henrietta,' which is a mouthful" is an acceptable sentence using a nonrestrictive which-clause to elaborate on the name, with mouthful as an idiom. Similarly, "I've always called myself 'Henny' because it's less than 'Henrietta' of a mouthful" is unacceptable in English because (1) mouthful is no longer in a correct idiomatic structure; (2) it now expresses a literal, not figurative, meaning; (3) mouthful is neither a place following a locative preposition of nor is it a possession following a possessive preposition of. In summary, when you alter the rule of how words or phrases are used and ordered, they take on different meanings. In this case, mouthful stops begin a figurative idiom and takes up a literal meaning.