Let me congratulate you on your purchases. The Harbeths are great speakers. As for the question about the Chord MScaler and Hugo TTs "brightness" I would say that is a misnomer. As you mentioned most things are very system dependent. So for instance, if you are running certain cabling that tends to transmit higher frequencies more prominently you'll more likely hear the high frequencies dominate the musical spectrum. The same holds true for mids and lows. Thus the "Weakest Link Theory."
My point is the Chord combo is one of the best in the world (in my humble opinion). That's coming from someone who has heard the dCS Vivaldi stack, Esoteric Grandioso D1, and other fine DACs. That said, I believe your Diablo 300 (once broken in) will produce a nice neutral and slightly warmer and organic sound that will have few peers in the integrated amp class (and I do mean few). And while when most read "warm," they think of excessive coloration. That's not what I mean. It just doesn't have a very dry, clinical sound that many of the integrated amps in its class have. Its signature is lively, without being brash. It's smooth without being pretentious. There's just a certain "right feel" to it that you can't put into words, you just know it when you hear it! Your transducers will benefit from that. And the Chord combo will give you nice depth and very natural sound staging as well, so they should mate very well.
Again, I wouldn't call the MScaler/TT2 innately bright at all. As a matter of fact, I think it is a bit more neutral than most other DACs I've heard with a very nice holographic sound staging.
For me system synergy is paramount. Make sure you get some very nice speaker cables, interconnects and digital BNC's for your Chord MScaler and TT2.
As for recommendations, I'm using Audience's Au24Sx ($2k+) speaker cables and XLR's (2K+), respectively. And as for digital BNC's cables, I'm using (3) Black Cat TRONS ($1,499/ea).
If you don't want to get everything at once I'd say wait or buy some "get by" cabling from a company like Blue Jean Cables until you can make the investment for some higher-end cables. But I would suggest auditioning as many cables as you can. I have found other manufacturers to be Audience's equal like Cardas Audio Crimson speaker cables and interconnects. But for my ears Audience is great! And more than likely the last cable I'll be purchasing for a while.
Sorry for the longwindedness. Hope you enjoy your system because it sounds like a really good one!