Perfect proof text for Paul not writing 1 Timothy

Recently, on Reddit's Academic Biblical subreddit, I'd seen claims that, yes, Paul didn't write II Timothy or Titus, but that he DID write I Timothy, and that language, and themes, were proof of that.

Let me immediately and swiftly demolish that; First, I Corinthians 7:29-31:

29 What I mean, brothers and sisters, is that the time is short. From now on those who have wives should live as if they do not; 30 those who mourn, as if they did not; those who are happy, as if they were not; those who buy something, as if it were not theirs to keep; 31 those who use the things of the world, as if not engrossed in them. For this world in its present form is passing away.

Clear and simple, right?

The passage obviously reflects Paul's belief in an immanent eschaton, spelled out almost breathlessly in what was likely his earliest book, I Thessalonians, but also found here, in Romans with the "ingathering of Israel" and elsewhere in his genuine epistles. (Don't forget, this is one of the main reasons II Thessalonians is considered spurious.)

Now, a famous, or infamous passage from the Pastorals, namely I Timothy 2:15:

15 But woman will be saved through childbearing—if they continue in faith, love and holiness with propriety.

Also clear and simple — and diametrically and totally opposed to the I Corinthians passage.

I just sunk the battleship of any would-be or alleged critical scholars who claim Pauline authorship for just I Timothy out of the Pastorals, and of course for the fundagelicals who claim he wrote all of them.