For the same "tech level" of bow, the longer a bow the higher the pull.
No. Definitely not true for modern replicas, let alone cheapos, and I do not see why it would be true for historical bows, either. When you have the luxury to make (have made) a custom bow, the length is decided by your height and arm length, and then you try for a particular pull by varying the thickness of materials and the proportions/mounting points. I'm talking about composite bows, of which I have three, one of which I helped make.
The higher draw weight short bows are laminated, composite or both
True, but irrelevant. If you do not have lamination/composite tech, there's only a few woods that can make a high pull longbow, and no wood that will produce a short bow that's more than a hunting tool. The composite bow would not have been developed in the British Isle, because there was no need. You can use longbows from horseback, and not just the asymmetrical yumi.
Long bows also used longer, heavier arrows which gives them both a longer effective range (the higher mass of the arrow makes indirect, plunging fire more effective)
A heavier arrow will receive less velocity from the same stored torsion (and the same energy) It will not go noticeably higher (and thus accumulated more potential energy), and it will not have a noticeably higher kinetic energy at the point of impact.
It is true that a heavier, longer arrow suffers less from air resistance. But the effect is minimal, especially since there no reason that a horse bow has to use lighter arrows.
and a higher effective draw weight (the same draw weight applied over a longer distance).
Another common misconception. Few people realize that a composite horse bow bends in a COMPLETELY different way from a long bow. If I could still I pull my Hungarian, the distance between the tips would be barely half the distance between my hands. The angle formed by the string is such that I could not use a Mediterranean draw even if I wanted to.
I did not draw my horse bows any shorter than I drew my longbow. If anything, because I used a thumb ring, my draw was about an inch longer than it would have been if I were a medieval English longbowman who would not have known about thumb draw. Every archer usually draws to the same point, no matter whose bow he uses, and strives to own as heavy a bow as he can handle comfortably.