So, I finally got around to swapping out my 81-7 for a 707, and it's pretty much exactly the change in tone I was looking for. The 81-7 just wasn't built for the job, no matter how I EQ'd my amp. Sure, I could just add gain on the amp to make up for the comparatively low output of the pickup, but that just made my tone fuzzy and ill-defined. What I was looking for was more chunk, and the 707 delivered that. There's also a lot less high end rasp to it, which I'm quite happy about. Thanks to everyone for their feedback on this!