Greetings,
Since ¨mat¨ was so kind to make some clips (couple of months ago I remember the best clip, named ¨sloppy 96¨, that I have heard on this Web page, with his non-HRM amp), and present them here, it can be generally assumed that he invited comments from readers/members of this forum.  
It is easy to agree with all the above presented opinions on this thread.  Indeed, this particular HRM leaves something to be desired ... and it does not match the above mentioned ¨sloppy 96¨ sound, in my opinion, which is also shared by ¨mat¨ himself.  So far, so good ...
As people know, oh so well, everyone has some wishes in terms of HOW the amp should sound, so there is a wide spectrum of possibilities and options.  I do not favor Santana and Larry Carlton ¨smooth and buttery¨ sounds, but would rather lean towards Steve Ray Vaughn, Joe Bonamassa, Danny Gatton, ... more clean, more aggressive, more ¨edgy¨ types of sounds ... and therefore, naturally, EXPECT to hear that sound. 
This present HRM sound, as demonstrated by the clip on this thread, makes it neither to ¨smooth and buttery¨, nor to ¨clean, edgy and active¨ type of sound.  
It is not quite clear HOW would HRM device influence the clean sound, if one assumes that clean sound is created by CL1 and CL2 valve (12AX7) going into PI and power valves, that is, without OD valve, OD1 and OD2, in the circuit (or am I totally wrong on this one, could someone explain?).
As for the pickups, it is very clever that one participant mentioned AlNiCo II type of magnet.  I have heard two pickups made by ¨Genesis pickups¨ (Telecaster replacements), at my friends' who happens to be a friend of the fellow who makes those ¨Genesis pickups¨.  That pickup was awesome, indeed.  So, I would be inclined to check out Genesis pickup named Mr. Browney, as presented on this Web page
http://genesispickups.com/products.html   
Again, Mr. Browney is yet not available to me, but it shall be, hopefully soon ... 
Finally, I would like to praise ¨mat¨ for his excellent guitar playing skills, his nice phrasing, smooth style and dynamics.  I really, really enjoy his clips, because they are made by such a good guitar player ... that helps, indeed!  
Also, YES, please, give us some CLEAN CHORDS -- let it all hang out!  And, while recordng, make the amp a bit louder ... Volume and Master knobs at ¨1 or 2¨ really do not represent the true sound of amplifiers as they are meant to sound in the real world.  While cranking up an amp more, though, watch for the digital recording media you are using, since digital recording media distortion is awful.  Well, that calls for a bit more of sound recording skills ... but, hey, invite some good sound engineer to your home or prctice room, and let him make some good recordings.  You know, some of the degradation of amp sound quality also happens in poorly used digital recording media!
All the best, and thanks for making us all this knowledge and experience available and so helpful.  
Sven