It surprises me too, given that it's a modern pedal - but if backing off the pickup heights has (at least almost) fixed it, it may just have very low headroom. Probably the easiest way to find out would be to take your guitar to a shop that has one and see if it does the same thing. The Invader *is* quite a high output pickup (although not ridiculously so), but if you hit the strings fairly hard you might be just taking it over what the pedal can cope with. I had the same problem with my MXR Phase 90, although that's more known as a low-headroom pedal. I'm using fairly standard 15K bridge pickups too.
I don't think there really is an 'optimal' pickup height, it just depends on your amp, pedals, picking force, string gauge etc - but the Invader does have those stud polepieces so you may find it's more difficult to get it right with it too close.