Most contemporary Bible translations use "more" when translating SoS, however they get it from "מִיַּ֔יִן", which means here more-than-wine, in the text you can't avoid the "more-ness" with the wine -יַּ֔יִן is wine, מִ is a prefix that can mean many things - such as "from" or more than. The full phrase is used "love better than wine" with Hebrew words for better, thus it is natural to assume 1:4 means the same. You can't get away from wine though.
Your love, with you being singular and masculine. A king is singular and masculine, but I am inclined to agree with Ibn Ezra that he is not meant, and this is really a question of whether the second half is to be thought of as a chorus. If we say "no" then "the king" to you is jarring, having it in remembrance when it is happening now quickly is jarring, and the he-beloved doesn't seem like a king elsewhere in the book.
If "thee" is not the king then we clearly are meant to see a comparison between "thee" and the king, the king is there taking her to his apartments and she is still thinking of thee. "Wine" may therefore be being used to contrast the fine wines of the wealthy king and the love of "thee".
In addition, if we are to think of it as an actual event then it does not seem to have any ramifications to the story. Nor does the meeting of Solomon's - and interesting that we get a name now - carriage in 3:8 occur as we would expect. The grammar does not demand the "were" reading, but Hebrew is quite weak on that tense so I do not think it rules it out.
Is entirely of his invention - there's no corresponding Hebrew word - however if you take the hypothetical comparator reading of the verse, then the "even" emphasises the poetical point: to most, the king is the best catch, but she prefers her beloved.
In conclusion, it looks to me as a perfectly reasonable exegesis of the text.