I can provide a little insight to some of the points made here as I have a CAT Ultimate II (w/phono) on loan for a few months to compare to the Aesthetix Callisto/Io. Amplifiers here are CAT JL-3 and Wolcott P220 driving SoundLab A1's.
Because the JL-3's do not have balanced inputs, and the Wolcotts have an XLR connector but these too are not balanced inputs, I use a 10m RCA IC (Purist Dominus B) from the preamps to the amps. There is absolutely no problem with this cable over this distance...no hum, no noise, no radio station reception, etc. Perhaps I am lucky in my area and there are no noise producing appliances near my system as well.
On the issue of balanced cables only making a difference for long distances, this is not necessarily the case. I learned just a couple months ago how flat the musical presentation was when I tried a 1m RCA cable between the Io and Callisto. It was not a subtle difference at all. A direct comparison of RCA and XLR Kubala-Sosna Emotion cables made this very clear. Even the vastly colored and less resolving NBS Statement XLR significantly outperformed the much more refined Purist Dominus RCA in this link. The Io simply needs to run from its balanced outputs to achieve its incredible 3-dimensional presentation. Similar comparisons between the two cable types with the Manley Ref DAC into the Callisto were very subtle so it was not an issue of the Callisto being overly sensitive to needing balanced sources. All comparisons here were with 1m IC cable lengths.
On the issue of the CAT SL-1 maybe working with Aesthetix, this is not an issue as Aesthetix does not make amplifiers. Only if you wanted to use the Aesthetix Io phono stage into the CAT's line stage. And already I have learned it simply does not work well as the Io sings magic only through its balanced outputs. If you like the sound of the Aesthetix preamp, you are not likely to be a huge fan of the CAT preamp....and vice versa. Mixing phono and line stages here will be the worst of all cases as I learned through a lot of trials with these two product lines.
And concerning BAT, only the 5 series preamps have balanced-only connections. The 3 series are also truly balanced designs but they also provide single-ended inputs and outputs along with the balanced connections. I would think that some of the BAT amps would also have single-ended inputs to accommodate Series-3 preamp users with single-ended cabling.
As the CAT amps are prohibitively expensive, someone buying a used SL-1 preamp is not likely to be buying a CAT amp. And with the CAT preamp's somewhat analytical sound, perhaps a BAT or CJ amp would be a perfect match to bring on some of the dimensionality and warmth. The CJ's are all single-ended so they would mate well with the CAT preamp in this regard.
I think you need to be far less concerned with balanced vs. single-ended and simply try various combinations here to find a pairing that works for you.
One other thing on CAT phono stage driveability of cartridges: the Ultimate II easily handles the Clearaudio Accurate cartridge which has a 0.6mv output. This was with the volume control only at 10 o'clock or so and it was plenty loud and incredibly free of noise....very impressive. I am sure a cartridge at half this output would still perform with no problems at all here. I gotta believe the gains between the SL-1 III and the Ultimate II are mighty close.
John