Harry_Y, welcome to the club!
The TU-8200 is a great amp for desktop use and this is where I actually use mine. You are right about it being small enough, yet powerful enough, and with more than enough features to keep you satisfied. I do not know much about the new 8600 yet and have never heard it, however besides what you have already noted, since the 8600 uses 300B tubes, unless you are crazy about this tube type, which are quite amazing, it doesn't make much sense for desktop use, compared to full/main setup use. The 300B tubes can go for crazy amounts of money, with true WE NOS being almost impossible to find, at least at an 'okay' price. There are other options for the 300B out there for sure, but I've heard from those that love this tube type, that quality can vary, especially with some of the newer production. I've also heard that the 300B tubes can also get very hot, which may not be ideal for desktop use, depending on your situation. Now with that all said, the 300B tube is probably considered one of the best, if not the best, tube type for audio use in general and it has been highly praised for many years. I believe Elekit also has experience using this type in their other designs, so I'm sure the 8600, with nice 300B tubes, would beat the 8200 sonically. However, the question is, by how much and if it is worth it for you and in your system in the long run. Going off what you have stated, I think you made the right choice, plus in the future you can always try the 8600 if you want to, plus now knowing that you have given the 8200 a chance.
As an additional note, some of the power tube types for the 8200 also get very hot. In my experience these are generally the KT-88, KT-66, and 6550 in particular. If you are concerned about heat build-up in the case, which I was, and also which can lead to additional component ware over time, you might want to consider a passive cooling system to help dissipate it. Several users here, including myself, have implemented solutions that can help with this. If you prefer to not make any holes in the case, which may let RFI/EMI in, one option is to use tube socket savers on the power tubes, in order to lift them off the hood of the case a bit, thus creating less heat transfer from the tube to the metal case and thus eventually inside the case. Just be aware that most socket savers are for tube testers and not for HiFi applications, so choose wisely and let me know if you want some recommendations.
Let us know how everything goes and what questions you may have during your new journey with this amp.
Lucidreamer, I agree with you that the input tubes do change/alter several characteristics of the sound, such as signature and tone, and can really bring out the best in the amp. However, I also have to say that I've generally found that the differences are slight in comparison to what can be done with the power tubes, similar to HiFi Boy's experience. However, we must remember that in stock mode, there are many more easily available and different types of power tubes that can be rolled than within the direct 12au7 input tube family. In my experience, going from a KT-88/66 to a 6L6GC and then to an EL-34, gives quite a bit of difference compared to different brands/designs within the input/signal tube 12au7 family. However, as I believe you are experiencing with the 5814WA tubes, switching out of the direct 12au7 tube family will yield much more noticeable differences, often times better as well, and there are several types that I recommend. In particular, the Brimar 13 series, the Amperex 7316 (my personal favorite), as well as the Tesla and Telefunken ECC802S, all in addition to the 5814s, have given me much better sound, to my ears, than most 12au7s. As far as the 5814 family goes, my personal favorites are the CBS black plate and Westinghouse types; I have tried GE black plates and found it to be a bit stiff and emotionless compared to others, however they were not the 5 star. In general and across many different types of NOS tube families, I've found that the militarized versions generally will give tighter, more dynamic sound, with better highs and tighter bass, if not just a bit less sweetness and air overall than non-military types. To me they generally sound more solid state, which can be a good or bad thing based on the rest of the system and your preferences.
From my personal experience, the best advice I could give to anyone looking to do more rolling with this amp is to first zero in on which power tube types you prefer overall and then tweak the sound by trying various input tubes (from different families as well) with them. Also, a great resource is fellow owner and member Dimu, who has done extensive rolling in this amp, well outside the standard 6L6GC/12au7 family and with great reported results.
Happy listening all!