Hi Yordiyo. This aspect has been a problem since I first got my old TM36 and found this forum. When I say a problem I should really say "for some people". There are those who love that fuzziness. Others like myself can't abide it and have tried everything possible to remove it. I have had to accept that there is a level to which I can reduce it and no further.
People put it down to cheap Chinese valves. It isn't! You can replace the valves with anything you like and you may improve things a little but you won't remove it. We have had people using Wathen valves at >$100 per 12AX7 and considerably more for an EL84, and the results are still described as "subtle at best". (See Voodoo Jeff's comments towards the bottom of Page 5 of the Valve Swapping thread in the GM36 forum which also applies to the TMs and the new GM40D.) The roughness, perhaps I should describe it as "shrillness, is down to the basic design and it cannot be modded out, believe me I've tried! (See the Spice simulation and analysis of the amp's audio performance thread in the GM36 forum. It's very technical but it will show to what extent some of us have taken this before it petered out as I realised it is an impossible task to separate the different aspects, good and bad.)
A lot of the tonal balance is down to speaker choice and the H&K amps are very picky about that but it doesn't really cure the roughness totally. I personally found the amps, (I also have a GM36), unusable with Celestion V30s. I swapped to G12M Greenbacks in my old '60s Marshall 4x12 and it improved a fair bit, but I was never able to remove it and be happy as a classic 60s/70s rock player. (Sod that square wave high gain neck wanking malarky with its 4 stages of gain.)
Also, learning to understand the relationship between the different parts of the amp and their controls is crucial. The input is actually a solid state buffer which does a brilliant job of setting up the signal for the valve stages which follow without any possibility of affecting the signal. It has the dual function of acting as a clever built in overdrive pedal if signal level is increased above a fixed level and ultimately as a Tubescreamer type distortion unit if signal is increased even more. Following that is another solid state stage which controls Gain with the option of adding some shaping at higher levels. This then passes on its signal to the valve stages themselves. Of course the Boost is involved in this too as is the Lead/Ultra channel selection. The input buffer gain is increased in the Lead and Ultra selections leading it to give an additional source of distortion on top of the Gain stage distortion at higher levels, and the distortion of the valve stages which we try to introduce. If you have too much roughness try making sure your input level is turned down to allow the input stage to act only as a crystal clean buffer, your Gain setting is moderate, and leave the distortion to be generated only by the valve stages by turning the Gain up gradually until you get the tone you want. Play around with the different channels set to do jobs you would not imagine they were meant for too. The Lead channel with very low gain and input signal gives surprisingly different Clean/Crunch options to those channels.
There are a lot of control and tonal differences available by balancing the guitar signal level and the Gain control. When they first get a H&K TM/GM amp most people seem to think it needs to be slammed with guitar signal and the Gain whacked up in the Lead/Ultra channels to achieve that magical distorted valve tone. It really doesn't, there is oodles of gain on tap and it is oh so easy to overdo that based on your perceptions. You will get a lot of mileage out of trying the Lead channel with Boost off and lower guitar input signal levels then using moderate gain settings. You say you have used the lower gain settings but try lowering your guitar level right down to maybe 1 or 2, and don't forget the levels introduced by pedals in front of the amp. I would start without any others in play. Gradually increase the guitar level listening to the sound change as you do. Turn it back down and do the same with only the Gain setting to hear how the sound changes with both of those parameters varied separately. It only takes a little too much of either for the other to become ineffective. It's really a balance of the two which gets you to the tones you want.
The H&Ks are not like more standard simpler amps like the Marshall/Fender types, they are much more advanced in their aims and more complex in their schematics and they offer much more in terms of flexibility of tone. The down side is that it takes a lot of playing to really understand how to get the best out of them. And even then there is a H&K character which you can never completely remove. For my money that character is at heart a high gain metal one. The German engineers at H&K are after all - - - well - - - mainly Germans! And they have their fellow countrymen's basic taste for metal thrashing and head banging in their DNA. And of course they have a target market in mind when they design!
Stick with it and play around with approaches you would not otherwise use, they will be the key to tweaking the tone to more of what you are looking for.
EDIT: Should have added that of course the Power Soak setting is a part of this too. It is actually intended to be a tool to offer you cleaner sounds at higher sound levels and different higher gain sounds at lower levels rather than just a way of adjusting your level from bedroom to stage.