Ized, consider the Dimarzio Virtual Vintage Heavy Blues 2.
It has the longest name so it should help.
And... its a recommendation from TGP - WalterW (or was it Eagle1), he seems like a tech who does know quite a bit, has been recommending it. There is a guy on youtube who uses it... I haven't check recently but back when I was looking around for info on this pickup, there's only 1 guy using it. I pm-ed him about it - perfect for that smooth, singing shred tone.
As for cleans - its warm.
Its difficult to get both bright cleans + the compression that can help legato along. Kotzen uses a Chopper T.
You can try the Chopper but in all the clips from say, Ron "Bumblefoot" Thal, he seems to favour the bridge humbucker (a Tonezone) over using the chopper when it comes to tapping. The Chopper when used for tapping sounds quite percussive so I'm not sure you want that. The Chopper in neck sounds quite biting actually and the cleans sound decent - you can find clips of it clean on youtube.
I think the Chopper could be that middle ground that might satisfy thee.