I have the Manhattan neck (very similar to the half note) in a semihollow guitar. Great pickup, that is for sure. The cleans are unreal. So natural and sweet. By comparison, the Mississippi Queen is more cutting and more pickup if you will, while still being very classic.
Distortion and the Manhattan is a weird one though. It is so round and sweet that it does not react like most other pickups to my ear. I would describe it more like those 70s psychedelic fuzz sounds. Somewhere in the realm at least. Can be good fun and it stays defined, but not the crunchy cut you want IŽd reckon.
Maybe have a look at the Blue Note instead. Still sharing a lot of qualities, but designed with some light bluesy distortion in mind. Probably a better bet here. Would not even count the Nantucket / MQ out completely. Very versatile those.
You get the warmth and goodness that Shakey Graves displays there, but holding up bit more like the humbucker he uses under the gain.
If you had two pickups in the guitar a half note neck might be more of an option cause you get the bridge in there too, but as you only have a neck that thing needs to carry a bit more.
My thoughts on the subject at least.