To make a long story short, I don't really like the neck pickup on my guitar but I'm happy with the bridge pickup. The bridge pickup is a Seymour Duncan Full Shred. I have looked at the liquifier and the illuminator but I got to thinking; from a mixing stand point is there certain neck pickups that you wouldn't want to use with certain bridge pickups? I'm sticking with passive for both so that wouldn't be an issue, but I imagine there's other factors I should consider.

Aside from that, it's obvious that bridge and neck pickups sound very different. When doing leads, how do you go about mixing them together in a way that sounds natural?
This is a hard question to answer, as there are SO many variables.

The good news is, for recording, it doesn't matter whether or not the neck and bridge pickups are in the same guitar. You can just find a guitar where you DO like the neck pickup on, and use that for the parts that would otherwise use the neck pickup.

As far as sounding natural, I find if you think about your guitar track as a collection of parts, as long as each part is done with the same guitar, you're okay.

part 1 - rhythm guitar 1
part 2 - solo
part 3 - lead fills
part 4 - rhythm guitar 2

Don't use two guitars for part 1. Use the same guitar. But feel free to use different guitars for the other three parts. As long as they complement each other, you're fine. Even consider using different amps!

Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.