To address your points in order:
-Yes, the Zen Triode is not a serious amp, and relative to modern solid state designs will have lots of distortion, even putting aside its incredibly low headroom. The nature of this distortion is actually why many people like them, but it isn't accurate sound reproduction.
-Too many Steve Guttenberg videos. To say that amp is not good for parties is an understatement. Here is the deal with amps like that: they will clip the signal peaks all the time. The thing is, the nature of the distortion that occurs when it clips the signal is pleasing to some people. It compresses the sound and adds low-order harmonic distortion. All of that can make the content sound more mellow than it really is. However, a 2-watt amp is absurdly low power, even for people who are after that mellowing type of distortion. If you are after accurate sound reproduction, a single-ended 2-watt amp may be one of the worst amplifiers you could have picked. Also, many of the people who rave about that type of device also think that power cables and equipment racks also have a major impact on the sound, so they are not a reliable bunch.
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Here is a good alternative to the 2-watt amp. It is just 110-watts of clean A/B amplification along with all the functions of a receiver. Comparing it to the 2-watt amp is like comparing a new BMW M-class car to a Ford Model T. It will be way better than your temporary DAC as well; The Outlaw receiver is using a modern Burr-Brown DAC while that Audio Note thing is using an ancient Philips chip. The THD and noise on that thing will be atrocious by comparison.
-If you like the Cornwalls, that is great. As for the Yamaha sound versus the Tubecube sound, at low levels, they may sound much alike. The difference comes in when the TubeCube runs out of headroom. It will begin to distort, and that occurs at a far lower level than the Yamaha.
By the way, I would consider it a very serious design flaw for a loudspeaker if it paired poorly with a common amp topology like a normal A/B design which is the most common kind of amp there is. Luckily I don't believe the Klipsch speakers are so incompetent where the amp type makes a serious difference. It's possible that Klipsch heritage aficionados like the tube amp sound because the distortion 'warmth' takes the edge off of what are otherwise harsh speakers. But having to use an obsolete amp design to compensate for a speaker's sound character is pretty damning for the speaker. Most speakers don't need a distortion effects processor in the signal chain in order to sound good.