I owe an "Attila's Archery" horsebow, and a Spitfire. Also, I have shot the "Hwarang" Korean horsebow, imported by Thomas Duvernay.
Haven't had any contact with the three you have mentioned, nor the "Kaya" sold be 3Rivers.
The AA bow is very heavy, and produces a lot of hand shock (this was a kit bow, that I finished) It does fire an arrow, though. Quite fast.
The "Hwarang" is a nice piece, and it really smokes an arrow, too.
The Spitfire is extremely light, very colourful, and also puts an arrow out at a good speed.
The AA, and Spitfire have no arrow "shelf" that is, you shoot off your knuckle. The "Hwarang" has a larger grip that forms a type of shelf.
"Yumi" archery produces horn backed horsebows, but I know nothing about these, and haven't heard of anyone but the bowyer, who shoots one. Yumi's owner/bowyer does shoot his bows in flight shooting competitions.
Are you going to shoot with a thumbring, or use a finger draw?