Almost all of the recommendations will work well with the invader.
But with that much output you can also seriously consider putting a hotter bridge humbucker in the neck such as the JB (my favorite HB for the neck, period), the Custom series or the Fullshred
Depends on exactly what you´re looking for. The JB for example will be very thick and fluid under gain, almost muddy for some. But the cleans are also great (a bit dark and warm, how I like ém), and split it´s a near perfect neck single coil :headbang: