This is right in the ballpark of my own personal experience. I got my first H&K a while back. It was a TM36. I sought it out after I had played a GM36 combo previously when I auditioned a gorgeous little '05 reissue Gibson LP Jnr Special DC with P90s which I snapped up at the price. I fell in love with the sound of the amp as well but it was way out of my reach at the time. Then after a few months the rot set in and I had to get into the H&K range. Again I was very lucky and came across a virtually new TM36 head local to me at a price which was just beyond my comfort zone but I took the plunge and went all in anyway. I loved so many things about it that I then talked my wife into the big brother, the GM36 and eventually I went for that too.
The GM is a slightly different beast to the TM but they definitely have a close family resemblance in tone. The GM obviously offers more variation and control but, due to the similarities in sound including their shared weaknesses, they both make similar demands of their speakers. My first thought after the TM purchase was, what speakers do I use with it. I know from experience that speaker choice is infinitely more important than anything you can do with valves but I was out of cash. So I did exactly what you are thinking of, I bought two Harley Benton V30 1x12 cabs. For the money they are superb, you get the whole cabinet including the V30 for about the same price as just the driver from other sources. I absolutely loved the look of my "mini-stack" of the two cabs set one on the other with the TM36 on top, and the GM36 is the same size so could carry on the setup. I used it for a year or two trying to dial it in to the music I was playing and that is where the trouble started.
At first I loved the H&K rasp and upper end bite. The band I was in were playing some music where it really suited. When I managed to get the material choices to lean more to my own favourite area, real classic melodic rock from the late '60s and '70s, I found I just could not get the amp to give out a laid back creamy sound which suited bands like Free, Bad Company, Humble Pie, Faces, Stones etc. It stayed in your face with an upper hardness that just wouldn't be tamed. The speakers were plain wrong! In fact it may well have been the cabinets which were a contributing factor. While they are reasonably made they are not the heaviest and most sturdy material choice. That wouldn't go down well in HiFi for uncoloured sound with any degree of lower extension.
Since then I have mated the amp with my late '60s Marshall 4x12 cabinet which I restocked with Celestion G12M Greenbacks to preserve the original G12Hs. This is a much better match and gets closer to the tones I am looking for. I do think this is due in no small part to my cabinet having the original older Marshall Pinstripe grille cloth with the rubberised vertical stripes, the same as the original Bluesbreaker 50W combo uses horizontally, rather than the more open woven type they went over to. It takes off a fair bit of the extreme top and adds a useful depth.
One final thing I would point out just in case you haven't come across it yet. These are NOT the same V30s that H&K put in their own cabinets. Those are specially voiced for H&K by Celestion and in my experience they have a very different sound, at least in the H&K cabinet. One of the problems with Thomann/Harley Benton is that you can't always audition the gear before you buy it as no one really stocks it. That is an issue and adds an element of uncertainty to the whole process.
So, from someone who went down that very same route you are contemplating, I would advise think carefully before you jump. If your material and playing style requires a thinner more toppy modern sound then the HB V30 cabs might be a match, but they will not give you any real sense of depth for more classic material. You mention Bluesy tone. In my estimation the H&K is not the ideal amp to use for Blues, though it can get there, just not in the same way as the Marshall/Fender choices do. You must understand that the TM18 gives the designers limited choices in terms of their circuit configuration. It has only two 12AX7s to achieve their design goals. One triode must be used for the phase splitter, and that must be the less common Cathodyne type which uses only a single valve. That leaves 3 triodes to use with the third stage driving the tone stack direct without a DC Coupled Cathode Follower as more expensive amps usually use. The DCCF stage gives a particular type of melodic distortion of its own if it is mated in the right way with the right gain stage before it. (I know H&K use this now as I pointed them at the information online and, lo, it suddenly appeared in their amps and their marketing.
) This all has a direct bearing on the tone you will get when you go up in gain. It can become less creamy and more buzzy to my ears. Some will love it but you may not. The TM36 and GM36 have 3 12AX7s which opens up the possibilities to more refinement in their circuitry and that does show.
I don't know if you are aware but the H&K TM/GM range has a built in Clean Boost/Improved Tubescreamer type first stage built in. Try putting the Lead Gain up close to full and throttle right down on the guitar signal you feed into it. Vary the guitar volume control and see the variety of sounds you can get out of it. I always found that input stage very cleverly set up, and to be one of the most responsive areas of the amp. First it is absolutely clean and a perfect transparent buffer. (Please, no crap about "tone suck" which doesn't exist in well designed solid stage circuitry nowadays, and H&K do their sums and design work right). Then with increasing signal level it begins to clip on one side introducing even harmonics, (the start of your Bluesy area). Next, with larger signals it begins to clip on the other side too at a different level and beefs up. Clipping is done with a number of series zener diodes around the feedback loop of an opamp to soften and round off the onset. It totally blows away the £150 crap boutique "back to back diode" clipping circuits everyone worships and which any decent second year electronics student can knock out in his sleep. This completely prevents the opamp which is the basis of the stage from touching its supply lines internally which is one of the major source of harsh tone from SS stages. It is a clever tool to get a range of clipping distortion modes from a single circuit, and it's built into the amp! Don't use a distortion pedal, just learn to use that input stage with your guitar volume control and the Lead Gain control and internal Boost switch.
I don't know if any of that helps, I hope so. They are great amps but they have their limitations and the synergy between them and the attached equipment in both directions is crucial to getting the best out of them.