I have Phi TC but never got to try it with TT2, which did drive Audeze LCD 2 just fine IME. So TT2 does not seem to lack power or control driving Phi TC as headphone amp? (presumably you drove it from front 1/4" headphone jack, not the rear XLR preamp outputs?).
As far as TT2, it seems like owners eventually end up with M-Scaler or are saving up for one

After reading a lot about Chord Dave and TT2, I get the impression Chord paid extra attention to the BNC digital inputs, and even without M-Scaler feeding the BNC inputs, I have seen some reviews mention they felt BNC input sounded better than the USB input in their systems. So trying out a well-made usb-to-spdif converter and feeding the TT2 via BNC may be something to try.
Yes I used the front 1/4 to drive them.
It sounded incredible.
First, When comparing the Burson conductor 3 to the Chord Hugo TT2 :
The Burson conductor 3 was maxed out by the Phi TC, I was running it on 96 and sometimes 99 and you couldn't go higher. So for that reason alone the conductor 3 isn't an option.
They still sounded great, They still had amazing bass impact but it was less clean and less detailed than the TT2. And it was a noticeable difference.
When comparing the TT2 to the Dave, mscaler, formula s and the powerman:
The TT2 had less control, It sounded messier, harsher & brighter / sibilant, The TT2 also didn't sound as full.
HOWEVER
It wasn't the same difference as it was going from the Burson conductor 3 to the TT2. It was a much smaller difference. It's a difference that I can happily live with because I am not missing out on that much.
Yes if money wasn't a problem for me I might have gone for that system just to get that extra detail and fullness, But again it's not a huge difference at all.
And the TT2 sounded as good or better as the Abyss stack - The formula s, powerman and the sagta dac.
For the TT2 to bring so much for literally almost 1/ 5 of the cost of the Dave system is insane!
The TT2 had amazing control of the drivers and he made the Phi TC and the LCD4 sing, Honestly that was insane.
With the LCD - 4 it was a match in heaven it was perfect! If the LCD-4 had the bass impact of the Phi TC I would rate them 100%.