Interesting passage regarding Pharaoh Amenhotep II and composite bows
" ...[he] drew three hundred of the bows hardest to bend in order to examine the workmanship, to distinguish between a worker who doesn't know his profession and the expert.
After choosing a bow without flaw which only he could draw ... he came to the northern shooting range and found they had prepared for him four targets made of Asiatic copper thick as a man's palm. Twenty cubits divided between the poles. When His Majesty appeared in his chariot like Montu with all his power, he reached for his bow and grabbed four arrows with one hand. He speeded his chariot shooting at the targets, like Montu the god. His arrow penetrated the target, cleaving it. He drew his bow again at the second target.
None had ever hit a target like this, none had ever heard that a man shot an arrow a target made of copper and that it should cleave the target and fall to the ground, none but the king, strong and powerful, as Amen made him a conqueror."
It suggests extremely high draw weights were available around 1460 BC and 300 suggests some sort of production line.
Maybe higher tier elite units could be given the full whack - range and power and of course a higher cost as it took months to make a single comp bow and they had to be cared for not a nice bit of kit you would hand out to a bunch of yokels.
Making HA's effectively have the same range as javelins with far less power = people will recruit/hire javelin cavalry instead unless roleplaying historically.