The CS neck certainly is great, but from what I hear the MM neck is also pretty nice. I would look into those aswell. Donīt know if they work for what you want but I would give them a look to be fair.
Cover vs no cover is a thing where, yes, there is a difference, but it is small enough for me to say I go with what looks better, cause I can dial in the difference elsewhere rather easily.
If I was just going by sound I think I would most of the time go open bridge covered neck, cause that is the way I roll.
I might like my neck PUs to be bright in the sense that I donīt want lots of low mids and lows, but I do find that slightly rounded top end to be very nice for my lead playing to smooth it out a tad.
Oh and yeah, everyone at BKP is super nice, helpful and really interrested in getting you what you want if that is in their power.
Was always so happy to recieve good recommendations and slight custom stuff like getting a regular P90 in HSP90 format.
The forum is just amazing too, so open minded, friendly, help- and respectful. There is a reason I am slowly coming up on 1k posts and still loving it.