StoneyB explained that the Cambridge Grammar of the English Language defines "when" as a preposition" which should be followed by an objective pronoun (such as me, him, her, and us) rather than a subjective pronoun (such as I, he, she, and we).
You didn't provide a link to @StoneyB's explanation, but I don't believe that by treating 'when' as a preposition he meant that it should be followed by an objective pronoun. When CGEL says 'when' can be a preposition, the definition of 'preposition' is expanded to include cases where a preposition can take a finite clause such as we met here. In traditional grammar, a preposition cannot take a finite clause, so 'when' would be classified as a conjunction in your example.
Therefore, 'when' being a preposition in CGEL is a red herring in your question. The real issue is whether it's correct to use you, me, Tony, and Gabi met here as a finite clause. And the answer is, it depends on how you define 'correct'.
The general rule of thumb is, you can use me as a subject of a finite clause, only if in a coordination. Your subject is in coordination, so your use might be correct. But some speakers might object to using me except when it's the first component of the coordination. So this would sound better to them than your version:
me, you, Tony, and Gabi met here
As others have noted, using I would be better to some speakers, but in this case, I should be placed at the end:
?I, you, Tony and Gabbi met here
?you, I, Tony and Gabbi met here
?you, Tony, I and Gabbi met here
you, Tony, Gabbi and I met here
Having said all that, it's not uncommon in casual speech that a native speaker uses me as part of a subject in coordination with me not necessarily located at the outset. So you're not alone in feeling you, me, Tony, and Gabi met here sounds okay.
As a side note, I don't particularly like your second sentence:
He deigned to correct something I, whose English is my first language, texted...
I think it's confusing to use the verb deign like that.
Also, you might not want to say:
my English is my first language
Instead, you might want to say:
English is my first language
So it'd be better to say:
...to correct something I, whose first language is English, texted...