I don't think any of your four options answer your question. From an Orthodox Jewish perspective, the answer to your question is that each verse serves a different purpose.
In the Torah -- the Five Books of Moses (Genesis through Deuteronomy) negative commandments (i.e. anything that says, "thou shalt not...") are brought out in two separate verses -- one that discusses the crime or sin, and a second that explains the punishment or consequence of doing the sin. In the example you gave, the first verse is there to make male-to-male anal intercourse a crim, and the second verse defines the penalty. The same is true for the two verses you cited concerning menstrual purity. Another example, the commandment to not testify falsely is given at Exodus 20:13, and the penalty for violating the commandment is given at Deut. 19:19.
The rabbis presumed that there would always be pairs of verses linking a crime to its punishment, and they used this presumption to explain difficulties in translation, especially where a word seems to be misplaced in context with surrounding verses. For example, Exodus 20 -- which describes the Decalogue -- lists several crimes for which the death penalty is called for (penalty listed in parenthetical), e.g.: blasphemy (Lev. 24:16), sabbath violation (Ex. 34:15), dishonor to parents (Deut. 21:18-21), and adultery (Lev. 20:10), in addition to false testimony, cited above. Two commandments at Exodus 20:13 bothered the rabbis -- לא תרצח (literally "do not kill") and לא תגנב (literally "do not steal") seemed out of place because (a) there was already two verses out there about stealing and the punishment thereof, and the crime of stealing property is not a capital crime), and (b) "kill" is a vague word -- sometimes killing is not only permitted, as in war or self defense, and, when done without clear intent to murder, would only be subject to a fine (see Ex. 21:18-27 and Babyl. Talmud, Bava Kama 83b-84a). Context should dictate that these verses describe capital offenses as well!
The rabbis, therefore, analyzed the verses in context with the pairing of commandments prohibitng an act with another verse describing the punishment for the crime. They determined that rather than "kill" the word תרצח should be understood as "murder" that is intentional and motivated by hatred, because murder is a capital crime, as explained at Ex 21:14-15, and there is no other verse to pair it with to simply describe the crime of murder. Similarly, תגנב could be understood as a prohibition against kidnapping (i.e. stealing a person), for which there was also a verse providing a penalty (Ex. 21:15-17) without a separate verse detailing the crime. See Bably. Talmud, Sanhedrin 86a.
I realize that there are people today who want to rationalize the Torah commandments to justify modern behavior that is inconsistent with the plain meaning of the Bible. You cited two rationalizations popular today -- association of a commandment with idolatry, and explaining commandments as an out-of-date solution for hygenic or health issues. The fact that homosexuality is discussed in close association to commandments prohibiting idolatry does not mean that because today idolatry is less of an attraction to people, all of the related commandments should be chucked. Indeed, every prohibited act mentioned in context with idolatry is as forbidden now as it was then.
With respect to "health" concerns -- you mentioned the laws related to menstruating women and their husbands, and others mention dietary laws in the same context. All in these cateogories argue that today we have hygenic and sanitary tools to make these laws unnecessary. But those arguments rely on the assumption that the purpose of the commandments was to solve health issues. Traditional Jews can cite to much different reasons which are too detailed to get started here now. We continue to observe these commandments -- and all others that we possibly can -- because God commanded them, and we do not try to second-guess God and suggest that the Torah is less than perfect by adding to, or subtracting from, its commandments. Deut. 4:2.
In light of the recent Supreme Court decision upholding the constitutional of same-sex marriages, I would like to add this amendment. My good friend Rabbi Gil Student wrote some interesting insights on the opinion from an Orthodox Jewish perspective. One of his points is that when the Torah was given at Sinai, Moses presented some new prohibitions regarding who can marry. For example, although Jacob married sisters (Gen. 29), and Moses' father married his aunt (Ex. 6:20), the Sinai commandments directly prohibited marriages with close relatives (Lev. 18).
The reaction to these laws came as a blow to families where near relatives were married and would now have to divorce. We find this hinted at Numbers 11:10, which tells us that "Moshe heard the people weeping, family by family." The Gemara of the Babylonian Talmud (Yoma 75a) interprets the phrase "family by family" to mean that the people were crying "about family matters," the newly forbidden relationships. Rashi, commenting on that verse, explains that the crying was about the new prohibitions above and beyond the seven Noahide commandments. The Jerusalem Talmud (Ta'anis 5:4), written well before the Babylonian Talmud, agrees that this is what the families were crying about.
However, Maimonedes (Mishneh Torah, Hilchos Issurei Bi'ah 22:18) seems to say that the people were crying over all the forbidden relationships, even those of the Noahide commandments. See also Babyl Talmud, Shabbat 130a.
Undoubtedly, the Jews who heard Moses give these commandments had the response: "What about love? Can't two people who love each other be married to each other." The Bible, however, tells us that despite the love a brother and sister might have for each other, or a uncle and niece, or two men or two women, the argument was not relevant to God. Whatever His reasoning, He made the rule and we follow it obediently, even if we subjectively disagree.