Old school is more of a game style -- I think you can achieve your intent with any modern rules system. Pick up a classic adventure for the flavor and run it using something you are familiar with.
That's probably true. I could do it with 3e, but I think I'd have to houserule it by stripping out feats and skill points. Death would probably be at zero hit points, and stats rolled on 3d6 in order. The latter are easy houserules, but by choosing 3e, I set up certain expectations with the players, and I'd then have to overturn those expectations.
The 3e rules also have the wrong flavour. There's too much player choice, they're too fun. I don't want fun. The 1e rules actually have the perfect tone. They are dark, gothic and oppressive.
The problem with 1e, for me though, is the actual rules. They're too slow and complex. I don't understand how initiative and surprise work in 1e. I don't want to look up attack and saving throw matrices. Or any matrices. I don't want weapon speed factors, or different damage versus S-M and L, or weapon versus AC.
What's your definition of "old school"?
For this game, my take on old school will be high lethality, quick PC generation, no builds, sandbox play, very gamist, very challenging, very tough. The world is weird, magical, and deadly. It treats the PCs like rubes at a 1920s carny.