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Crossbows have a smaller body allowing them to be used in smaller places more easily, such as inside a castle tower. The reinforced limbs of the crossbow (usually reinforced with iron) allow the smaller size to still have similar draw strength as the larger bows. Due to the more rigid limbs it is much harder to string a crossbow, requiring a machine or at least much more care. The usual method to string a bow places the bottom limb around the leg and bending the top limb with the arms, which makes it possible for a single person to string most bows. Reloading a crossbow would be similarly difficult due to the rigid body, which warranted the development of the hand-crank for reloading, which eventually became spring-loaded for the auto-reload referred to. (Though this would be certainly much later and not too long before early gunpowder weapons started making bows obsolete)

One of the other benefits not mentioned to using a crossbow is the projectile speed would be immediately at its highest after firing, making close-quarters a crossbow much more effective than at long range. This is also due to the projectiles themselves generally being small and heavy, such as small metal balls, shrapnel, or short metal bolts that may or may not use fletching for flight stabilizing. By comparison, an arrow shot at a curved trajectory from a longbow will be traveling at its fastest as it reaches the target due to gravity. This may not always be true depending on the relative heights of the shooter and target, but in general this would be the case. The longer arrow (usually) coupled with its fletching made the accuracy at range much more reliable than with a crossbow. In addition to this a skilled yeoman is able to judge the distance and adjust draw distance accordingly, whereas a crossbow has only one resting position and so only one firing distance, per se, not really accounting the trajectory angle since it was designed to fire fast and straight.

I'm not exactly a medieval scholar, but I certainly am an enthusiast. I am probably wrong about some of what I wrote, but largely it is what I understand to be the case in medieval combat.

As to the OP I think it all sounds lovely and I've always wanted the weapons to have more of a purpose to their diversity. To me, diversity without meaning is like having green and purple grapes that both taste the same and you are colorblind anyway.