First of all, the verse doesn't need to give exceptions. You're trying to give the word "all" some absolute sense that I don't see any basis for giving it. You demand that there be a specific contextual reason to limit it, but you don't think you need a specific contextual reason to make it unlimited. I don't agree with your aversion to parsing words. If you want to understand a passage and study it in detail, that's what you have to do.
Second, the passage does not say "all men." It just says "all." So if you're going to use your rule, then you can't just limit it to people, it has to mean every single thing in existence.
Third, even if it did say "all men," in what possible way could it be absolutely all people? Not everybody knows about Jesus or his crucifixion. How do you understand that by being crucified he draws absolutely all people to himself? Do you apply that to the final judgment when all people will stand before him or something?