hot enough that it gets a decent split tone, i wouldn't go hotter than 16k to keep cleans with decent treble. then again, depends on what kind of treble you prefer, if you prefer sharper treble to sparkling treble, you might like cleans of a 10k pup, but if you want that extended, sparkling sound, you might not like anything hotter than a 6k pup.
check out the steve morse model by dimarzio, the neck pup is wound so hot that it actually gets a drop in volume because of the drop in treble. however, it'll split to 10k, which is as hot as a really hot single coil. if i remember correctly, its also got ceramic magnets, which would give you more output and treble.
don't worry about pots or the switch. to hardtail it, jam something behind the vibrato. a guy named chappers on youtube has a great video on doing that.
also, when you say 'really heavy' that can mean allot of things. use better adjectives, and cite guitarists and clips as influences to help.
i was getting a 'really heavy' tone out of a plywood jazzbox from the 60's earlier today.