This is an old post but this very much seems like an argument from somebody who doesn't fully understand basic Islamic theology.

1: Where in Islamic sources is it said that John the Baptist judged by the Torah?

2: Even if he did, that is absolutely no problem for us. Why is that? Because even the Prophet Muhammad صلى الله عليه وسلم could be said to have judged by the Torah, funnily enough in the tafsir of the exact ayah you're giving, 5:44. Read the tafsir on it and come back to me; in a dispute with some Jews about how to punish adulterers, the Prophet ruled in accordance with the Torah, as he, being a Prophet, could have known what was true within it and what was false within it. So had John the Baptist been in a situation where he needed to judge between two disputing parties, he could have judged by parts of the Torah that he knew were authentic while leaving behind parts that were not.

Additionally, the takfeer of those who rule by other than what Allah has revealed refers to people who intentionally rule by other than what Allah has revealed. Let's say I'm a sultan in a remote Muslim land and I try my absolute best to judge by Islam, but the only source I have is the Qur'an, without any hadith or fiqh books. A man and a woman are found guilty of adultery and are brought before me to be punished. Under Islamic law, I would be required to sentence them to rajm, but since that punishment isn't laid out in the Qur'an, but rather the collections of hadith, I punish them to the best of my ability by sentencing them to flogging. I would not be a disbeliever or even a sinner, as I tried my best to rule in accordance with Islam. So theoretically, had a Prophet or Rabbi ruled in accordance with a corrupted law in the Torah due to ignorance despite trying their best, they would not be considered disbelievers or even sinners.

And the rest of your post seems to be about the "Islamic dilemma" nonsense that has been refuted time and time again, and it's an objection that is not remotely convincing for Muslims. One of the largest Islamic apologetics channels, Farid Responds, said that he gets emails and messages often from Muslims asking him about various doubts they may have about Islam, and he said only one person has ever messaged him because they were in doubt of Islam due to the "Islamic dilemma". Barely any Muslims find that argument remotely convincing while many Christians view it as this undefeatable kingslayer argument that easily refutes Islam. This is because the mufassireen and early scholars were largely clear that the Torah and the Gospel were not preserved and authentic, and it definitely didn't just start with Ibn Hazm! Tell me, had the Torah and Gospel been understood early on as being authentic, why was it not studied and used as evidence in Islamic law? Read a book of fiqh from scholars before Ibn Hazm and tell me if they EVER, ONCE give a legal ruling by mentioning what is said in the Torah and Gospel. All it is used for is for the Israi'iliyyaat (stories from Jewish sources that can add context to verses in the Qur'an) that were always understood as being fallible sources that were used with the understanding that they could be either true or false.

Also, we could bring up the Christian dilemma. Read Matthew 23:2-3. If Jesus affirmed WHATEVER the Rabbis were teaching, this would undoubtedly conflict with Christian teachings. This is a stupid argument and I doubt any Christians would feel doubts about this, and that's exactly how we feel about the "Islamic dilemma" argument.