As great as the Schmidt is, the Paul would probably suit your needs better and cover more ground. As above, the Schmidt has a good gob of gain, but the amp has more give and the bass is less tightly controlled than other Diezel's. So it's less 'CHUNK' and more 'OOMPH', if that makes sense.
Hot pickups and boosting can increase tightness a bit but I don't bother, opting to use pedals that add some hair and grit while preserving the feel. Though I will say, an EQ in the loop is massively powerful, helping to cut some lower bass frequencies and add some additional presence for high gain chugs, which the Paul thankfully has power amp controls onboard for.
Re gain tones: Ch3's high gain can get real close to Opeth's Ghost Reveries and Watershed. Full but a bit rounder/smoother/warmer and a bit more give. Which makes it an incredible accompaniment to any other Diezel. In addition to my VHX, I have most bases covered!