Great playing and tone, but if I didn't know you were doing a Tool video, I wouldn't have guessed it had anything to do with them honestly.
The riffs and production are maybe more like Deftones, the tone is gainier and more aggressive than Tool go for. The Tool tone to me is essentially a plexi, with the low end coming from the rectifier. The later Tool tone using the Diezel is basically that in one amp - the compression, crunch and midrange is like a cranked Marshall, and the low end is more like a Mesa. Micing the cab with a 421 gets the low end and mids sat right.
The multiple amps thing to me is mostly about changing up the amp for different sections. Combined with adjusting the guitar volume knob, it allows for a wider range of tones than any one amp would provide. There is definitely some blending going on, but it varies, and often its just one amp at any one point.
FWIW, this was my attempt at matching the tone from Rosetta Stoned (A/Bing with the original) with Helix and Fractal's VH4 models:
enjoyed the video none the less!