Philly Q tried the Black Dog bridge in an Edwards V and thought it was a bit meh. I have a Riff Radd in the bridge of a similar V and it work excellently for an open Schenker-y sort of tone. Maybe ask Philly Q for more details of his Black Dog'd V.
Yeah, I wasn't crazy about the Black Dog in the Edwards. It was a little on the dark side, although I don't think it was muddy. But a big part of the "problem" was that I combined it with a Stormy Monday neck, so I had a dark-ish bridge pickup with a bright-ish low output neck pickup, there just wasn't enough of a contrast for my liking (I've said that many times, apologies for boring everyone).
I should add that it was a
very lightweight V - I have a feeling that the BD might work better in a heavier, less resonant lump of wood, but I could be totally wrong about that.
If I remember right, the guy who bought the V from me (Marauder on this forum) really liked the BD, but I don't know if he still has the guitar or the pickup.
I agree with Jonathan that Cold Sweats are excellent in mahogany guitars like Vs or SGs - and I would stick with the CS neck pickup, I can't imagine anything else being a better match with the bridge model. If I was going for something lower-output, I'd probably pick a Riff Raff bridge with a Mule neck, or maybe a set of Mules. I don't know about the VHII, I think of it more as a Strat pickup (can't really explain that, it's just how I think of it) but I expect it would be fine in a Gibson.