On second thoughts, I still don't think it would work.
As you tilt the cup towards your lips, if the "highest" siphon pickup is still submerged, then that will correspond to the "lowest" siphon top and it will start siphoning anyway.
It would work as long as it could be arranged that the pickup would become exposed to air before the siphon started siphoning, but I'm not sure that's possible while still retaining the property that it self-starts when overfilled.
Also, even if the tube doesn't siphon because the pickup is exposed to air, there would still be liquid in the tube, some of which would get pushed over the top and leak out the bottom whenever you try to drink.
The high point of each siphon could be exactly opposite the entry point.
The siphons would need to cross past each other, but only 2 at any one point need to cross, which I think is manageable.
Maybe my Pythagorean cup rabbithole is still not over...