I mean, you’ve pretty much laid out the options. There isn’t a lot more to say.
I’d comment that time stop is not instantaneous, even from the outside—technically it speeds up the caster an immense amount, but some finite amount of “real” time does pass. So if you double that time, and the time stop caster is still sped up just as much, they should have twice as much “apparent time” to work with.
And, for that matter, nothing in Extend Spell suggests that it only applies to “real” durations—it doubles the duration, whatever that is, or at least so long as whatever it is can be said to have a “length.”
So RAW, my feeling is that extended time stop—and worse, persistent time stop—is legal. That doesn’t mean the designers intended it, that you should allow it, or that you can expect anyone else to allow it. The RAW isn’t precisely air-tight, and in any event, RAW isn’t necessarily the same as intent or how things “should” be run.
As for what I would personally do, it’s kind of moot for me—I don’t run games that get anywhere near allowing 9th-level spells, and speaking hypothetically about games that do... does it even matter any more? You have 9th-level spells, and you can apply metamagic to them somehow—you’re already well past the point where 3.5e can have any claim to balance, or even stability. It’s a monstrous effort to even have a coherent campaign at those power levels, even with cooperative players.