I remembered having trouble with this one too, so, after reading this, I broke out SSB and gave it another whirl, after having been an SSBMer for so long. I managed to get it first try. Hehe, I still got it. [/ego inflation]
Anyways, the way to get it is what your second method was. Jump from the top middle. Timing is crucial. You need to jump off the platform JUST before you run off the edge and fall off. I fell off 3 or 4 times doing this just now trying to get a feel for the timing. Get a good idea of when you need to jump to get maximum distance, the more ground you cover with your jump, the less air you'll cover, and the less likely it is you'll make it. Also, time your jumps well, particularly the Screw Attack, as I believe you fall faster than normal after using it. Done correctly, you should be able to Screw Attack onto the left edge of the platform and just barely get above it, then when you fall you'll of course hit it and end the stage. It's all about timing really, there are no tricks that make it easy, that I know of anyway.
EDIT: An "is" ran away from me, needed to drag it back into its place.
EDIT #2: Gave it another try, I made a hopefully not too bad error in my description, the Screw Attack should bounce you ONTO the left edge of the platform, not through it, my bad.