Animals and Pets

I adopted a new kitten approximately 4 months ago; Mister Black. He was an older kitten, and has had persistent diarrhea since I brought him home. I don't need advice in this regard - all options are being explored with a vet and I've spent many hours trawling the web for potential solutions. The vet's opinion is that he's all-around healthy, minus the diarrhea.

He's got definite crackhead energy, and receives plenty of play to wear him out to the point of panting. Still, he will occasionally go directly from cuddling to biting or clawing my legs. I'm starting to suspect his original home may have played with him using their hands. I respond with yelps, removing myself from the room or re-directing to a toy, but it doesn't have any lasting effect.

I already had another cat, Mister White, who's frankly spoiled me with his good manners and gentle spirit. I've had him since he was a tiny kitten just ready to leave mama, and he's a year older than Black. The two of them can hang out supervised, but White distrusts Black after he's tried to roughhouse one too many times. They were introduced slowly with scent swapping. Their playstyles are completely different, so I haven't managed to find a way to play with them together (Black enjoys adrenaline and muscle play, White enjoys stalking and chases with no contact). They can eat together just fine, although Black has to be actively discouraged from eating White's food.

Black is being castrated next month, which I'm hoping will help alleviate some of his issues (It's taken this long due to waiting for his medical issues to resolve). But I'm concerned that it might not - in which case, where do I go from here?

tl;dr: kitten is Satan and old cat is Jesus, what do?

ETA: It's worth adding that I have 18 years of experience with cat ownership with multiple different cats, and I haven't experienced anything like this before.