Trivium and Nevermore have very different tones, but it's mostly related to differences in guitar and amp as opposed to pickups. Nevermore uses extended scale guitars so if you don't already have one, look into a baritone scale guitar. They also use ENGL amps now, but they used Dual Rectifiers for a good majority of their earlier album tracking. AFAIK, Trivium on the other hand uses 24.75" scale guitars (shorter than normal) and LP body style. I think that Trivium uses JCM 2000 DSL amps too. Both bands use EMG 81/85 pickups, so the tonal differences are not really pickup related.
Anywho, enough rant. I am thinking that in your basswood 7 you're going to need some low end, because the wood is not really that bass heavy, contrary to what the name may imply. The guitar is also not extended scale, so some low end isn't going to hurt IMO. Cold sweat bridge might not be for you, but it might not be a bad idea for the neck. I am thinking maybe Ceramic Warpig in the bridge for the high output to match the output of the active pickups that they use.