You could go with a spring mechanism, with a winch to draw back a hideously strong metal coil... or you could make it a Gauss crossbow, propelling the bolt along the barrel with whatever technobabble strieks your fancy.
Also, I don't think fletching per se has to impart a spin on the arrow, it ensures that the arrow does not tumble.
As it is, the technological solution does not make too much sense.
On a different note - you can really go way out there: what if the bolts are magnetic - and coincidentally, the magic used to enhance the armors of the cavalry improves all the properties of the metal, including attracting magnets, disproportionately so?
You know, I really like the concept here. It isn't wildly different from your standard demonic pact, but I don't really mind. I like how you took a relatively simple idea (sorcerous magic comes from a possessing spirit) and really fleshed it out to fit within your world. Well done, and thanks for the enjoyable read.
Ultimate power, a bit of madness, the risk of dying horribly... what's not to love about this.
I like the flavor that bleeds through. These aren't normal sorcerers who gather power through bound spirits. There is an entire ecosystem of ethereal creatures. It speaks to a larger, well-developed world, with enough similarities to standard fantasy to make it easy to grasp and enough uniqueness to set it apart.