You can absolutely add a TS in there if you'd like, but turn your gain down. Most of the guys using them in front of high gain amps are using them as an EQ + boost with very very little of the actual distortion coming from the TS (crank the level up and use the Tone knob to set it how you want). You have the master volume thing backwards. On high-gain amps, the more master volume you use, the muddier and flubbier your low end will be. I probably run a bit high, but I like more MV power.
AMP (block) - Axe-Fx II Wiki
What you're hearing there is layers of gain. Not a single channel with the gain cranked. When you double track, the gain really stacks up fast. I agree with you about pick attack, but try flattening your pick a little to get more of that fat, strong sound with less scraping. That pick attack is around 1khz btw, so you can dial in more of that scrape sound without all the gain with a bit of PEQ around that frequency.
Mic sims are preference. I don't use them, but other people do.