Alright, I'm just going to throw all of my ideas out at once, so sorry if my mind dump ends up rambling.
First off, I also like the crossbow concept because I believe that the magic should be in the weapon, not in the missiles. This can lead to some interesting effects when a party first uses the weapon with normal bolts, with no consideration for the type of feathers (or mixture of feathers) used in their creation. I can picture the crossbow as having one or two birds wrought in metal with overlapping wings and tail feathers, providing a sort of wrist guard. Perhaps the appearance of the birds could shift slightly, depending on the type of feathered bolts used to load the bow.
Religion based on bird worship -- could work, but can be taken in very different directions. On one hand, you may have a church that will use only images & carvings of birds, and would consider using their body parts blasphemous. Might burn them ceremoniously (including arrows with bird feathers). Most crossbow bolts from areas like this will be plain wooden ones, with possibly some stiff brissles to aid with their flight. A different approach, of course, is the church that will ritualistically sacrifice birds to the gods, adorn their priests with elaborate feathered head-dresses, and consume chicken every week on their holy day. Your choice, really.
The only thing I see in common between the two approaches is that the bird imagery will be strong in all priestly vestments. A bird priest would probably look quite garish, compared to those of other faiths, with his many-colored robes and jewelry designed to imitate feathers. Or then again, priests may dress as different birds, depending on church hierarchy. I can imagine that the head priest may want to closely resemble an owl, perhaps with large ornate spectacles or some sort.
Moving on: falcon feathers could be used to fashion a bolt that always flies true, or is faster than normal bolts and so harder to dodge. Kookaburra feathered bolts might cause an uncontrollable fit of laughter, to the point of incapacitation.
One final note. Perhaps you should give some thought to how the crossbow will react to feathers that have been taken from the bird by force, rather than given willingly. Being created by a bird-worshipping religion, there may be some serious consequences for using bolts with feathers from murdered fowl, to the order of a light curse. This will also keep the PCs a bit better in check, as they won't automatically go killing every winged beastie in sight in order to try their feathers in the crossbow.
OK one more -- love the ostrich feather arrows, but bolts made from them would have to be quite large (seeing as how the feathers themselves are). I'm betting that this crossbow would end up being considered a heavy crossbow, with most of the significance/penalties inherent to your gaming system. Alright, I'm done now.