are you using 500k pots? true single coils tend to be a little shrill with 500k pots.
if you are using 500k pots then i would suggest something like the ssl3 hot model or a lil 59b for the middle. the hot is fairly middy with 250k pots but with 500k pots its much more open and since it is higher output you can keep it lower from the strings so it wont interfere with picking. the lil 59b is a kick as tone in the middle but not very single coil like
i think its 250 not sure really...coz the jaz/jb on my guitar was done by my friend (very good at wirings) and he havent told me anything about that...
I set up a jazz/Cool Rails/JB combo in a friend's Ibanez S470 and he wsa very happy with it. The mid CR was nice and spanky and had nice twang when combines with the parallel JB in the bridge.