If the pickups are the EMG HZ types in it, then you may have a problem as they are bigger than dimarzio or any other maker's 7string pickups, in which case you may need to get some oversized pickup rings, this is a warning, as i just looked at the schechter site, and it looks like it;'s routed for emg 7string size pickups. Why they did this i don't know, but their casings are larger than normal 7string pups.
Anyway, I'd avoid the Tone Zone 7, it really does sound quite lousy, not a patch on it's 6string cousin. I'd be dubious about in general after my experience with it, but it may work in basswood, although i am dubious.
Blace Customs are nice little pickups, work well with lots of midrange to play with, although i found as with the blaze bridge that the low end can get a little flubby and undefined, so if you are looking for tight, then either go with an evolution 7 (although that is hot, but very clear) or try out the Drop Sonic7, as a lot of people are loving that pickup it seems (also very close to the petrucci EBMM model, either that or the blaze custom, i can never remember)
Also, you could think, strangely, of the blaze (neck) pickup for the bridge. A few people have said good things about it, it basically being a hotter paf in a way.
Neck pickup wise, PAF7 is good (also good in the bridge) and i know the Jazz7 from the seymour duncan side gets lots of good things said about it, although it is a tad hotter than the paf7. Otherwise play it safe and go with the Air Norton7.
To be honest, I'd read the pickup review thread on sevenstring.org as it will cover all those pickups in the wood type you are looking for, and somewhere on there there's a guy that had the overasized pickup rings to convert back from EMG size routing to normal routings. Curse you EMG!
Hope that helps
James