Is elliptical the best stylus profile

Chakster's remarks are spot on — it should be published separately somewhere. I don't disagree with you that a good elliptical can equal a more advanced profile. Much depends on the minor radius. An 0.2 "reads" as much of the groove as the fancier stones, though record and stylus wear are not as good. The thicker that radius, the less resolution, and at a certain point it's just a variant of conical. Years ago van den Hul introduced two styli, VDH 1 and VDH 2. One would think the 2 was an advance on the 1, but it was the opposite. The VDH 1 was so detailed because its edges were razor sharp — consumers were so afraid (unjustly) that it would carve up their records, he had to make a "fatter" diamond to stay competitive. But alignment is more critical with the sharper profiles. Chakster is right about the Hyperelliptical — I have one on a Shure IV (I don't like the cartridge, but that's how it goes — I may transplant it onto a cart I like better). The Hyper is almost a line-contact, tons of detail and nuance, while also easier (and safer) if you're not confident the alignment is exact. 

"Is there any correlation between stylus shape and a specific alignment method for setting up the cart?"

No. Aligning the stylus has more to do with the record groove than the stylus. There is one position, and one angle, in the groove where the most information can be extracted, with the most accuracy, regardless of stylus shape. Once the stylus is in that position, its shape will determine how much of that information it is able to extract, but "finding the spot" is the same for all shapes.