I apologize, I didn't see this question until now. I have had extended listening time with every product in the Cavalli lineup, so I can answer pretty much anything you want to know about them.
The three amps you've mentioned here are all absolutely terrific. The iCan Pro is a terrific value and will power anything you throw at it. It sounds fantastic with the HE-6, for example. It really shows it's stuff with a great DAC on the front end. Tons of versatility with the adjustable tube and stereo expander settings.
If I were to associate one word with the Questyles, it would be clean. I mean just super spacious, ultra squeaky clean sound. Really comes across as a true reference device. Almost zero THD. One of my favorites with the HE-6, HD800 and Dharma.
The Liquid Crimson is all about air, ambience, massive bass impact and gobs of rock n' roll soul. All of the Cavalli amps have a slightly different flavor and set of strengths. The Liquid Crimson really works best with slightly darkened orthos. It is the best amp, bar none, for the HE1000. People at Cavalli and Hifiman both seem to agree. It also does wonders with my modded HE500 and I'd be willing to bet it is absolutely stunning with the LCD-4. It is also stellar with the Beyerdynamic T1 - both V1 and V2 - I don't particularly like them on anything else. The Crimson is a little shy on power to really make the HE-6 and the Abyss shine, though. Those are really more well suited for the LAu. Same goes for the HD800, which benefits greatly from the warmer sound and the best-in-class treble control of the LAu. The 800 still sounds good on the Crimson and all, but the Liquid Gold is just so much better with them.