It's all fun and games until you come home to bloody battle. I'm not picking on you, but I've seen what happens when people don't take this seriously. All it takes is a couple flyes with a long spurred cock, for Legs to lose an eye.
Asils, like all gamefowl are bred for competition not uniformity. Yes they share traits people think help them compete, but that is not their main purpose. All the birds you presented are likely Asils, just from different hands. I know this doesn't help you clear things up though.
The lack of hackle feathers on the Bekisar looks very oriental like. A highly inbred junglefowl crossed over a few times with a Bekisar could give is the birds we have now. Except there is no accounting for the drive. But wolves don't have that drive and there are game dogs out there, therefore...
They could just be VERY inbred junglefowl. Looking at the parrot-beaked asils. They are a more extreme oriental. One could then assume that inbreeding for years and years like many oriental breeders do, would create the bird we have now. And just crossing with other Gallus strains would add to that.