You are right, many of the requirements are contradictory... it also depends what the projectile is... a flight arrow or a 1/4 pound war arrow.
For flight bows I personally favour short limbs, but with all the limb working, on a shortish bow, but then, that limits the available draw length.
the other big factor is longevity, there is a world of difference between a high stressed flight bow and a long smooth ELB target bowor a heavy weight warbow.
Depends how you defend efficiency too!
Even limb cross section isn't an easy choice, a rectangular (but lightly rounded) 5:8 depth to width qualifies as an ELB and is lower stressed than a deeper section, but the deeper section being higher stressed stores more energy for less mass.
It's all a compromise... and don't even start on adding a bit of deflex or reflex!
Del