You have an outstanding setup here......don't compromise on the cables. One key area that so many ICs destroy in the preamp-to-amp link are the decays, ambiance, harmonic overtones, etc. You have this capability in spades ..... don't throw it away with mainstream cables.
I have found two ICs that work incredibly well between the Aesthetix Callisto Sig and CAT JL-3 amps: Stealth Indra and Jade Audio Hybrid. The Stealth has a little more extension on the top; the Jade Hybrid portrays the 3D and decays more beautifully. These are both in the $2k range but to go for something with much less performance just does not make sense here.
For speaker cables (I have SoundLab A1 speakers), surprisingly I find the Purist Opis to work very well ..... no obvious tonal peaks or valleys and quite good in dynamic contrasts.....the latter is the key strength of the CAT amps. The other speaker cable I have heard that stands out is the new Jade audio but it runs twice the price of the Opis. This fleshes out the 3D in the music much like the Hybrid IC.
Give the Jade cables a listen. You can try them out for a month no obligation and you will likely be mightily impressed.
Once you find cables that work, I can give you some tips on small-signal tubes for the CAT amp that will take it far beyond the stock Sovtek and Ei tubes.
John