There are so many possibilities. One generalization we can make is that the engine is dying when vertical because it leans out in that position. Flyboy Dave mentioned low compression. I agree with him, there's no reason to take the entire engine apart, unless you have low compression, which might give the engine marginal fuel draw, causing it to die when vertical. Usually, a low compression condition will make the engine hard to start and not idle very well, if at all.
A more likely cause would be the needle valve adjusted too lean or an air leak of some kind. The needle valve should not be adjusted for maximum rpm. It should be a little richer than maximum rpm, perhaps 300-400 rpm less than max. would be a good starting point. Others might disagree with that number, but everyone will agree that it has to be somewhat richer than max. rpm.
An air leak could also cause marginal fuel draw, which would be worsened in the vertical position since the fuel would have more vertical distance to travel. Air leaks usually occur in the following:
1) Needle valve threads loose in the housing (can sometimes be cured with a short piece of fuel tubing around the needle valve to make a seal where threads and housing meet)
2) Carburetor to engine joint (try a new 0-ring, and pushing down on the carb. while tightening the draw bar)
3) Engine backplate leaking (try a new gasket or 0-ring, and tightening the screws)
4) Leaking seal on the front engine bearing (requires disassembly and replacement of bearing/seal)
One more thing to check. You said you removed the fuel tank, but you did not say if you DISASSEMBLED the fuel tank. I suggest you check to make sure that the pick up line and the pressure line are not reversed, that both lines inside the tank have no holes/slits, that the pick up line did not get jammed/bent forward and stuck that way from a hard landing or sudden stop, and that the pick up line did not get disconnected inside the tank.
I know some of this is very basic, so forgive me if you already know it. I just don't know how much you know, so I'm trying to cover all the bases.
Good luck, and please keep us posted so we can all learn what worked and what didn't for future reference.