Finch,
I upgraded to HR-1 from 944s with my Torii III. Now I have a MKIV with the HR-1s and am currently using a Blue Torii with my 944s. I modified both speakers to suit my sound and room. But interestingly, in both of my rooms, the 944s sound pretty close, the second room the speakers out from the walls more. Both speakers were too bassy and dense sounding in this room with the MKIII, but I know from experience of room work, and I suspect from other posts, the room makes loads of difference. I also likely prefer a little less "warm," and a "faster" sound.
Treated pretty similarly, the HR-1s are more refined and spacious here, with a bigger feel, and they excel in some ways (like drum and piano authenticity) but they are really very similar. The radial addition is very artfully integrated and adds a really good thing, but in my main system/room, both had about the same soundstage and roughly the same tonal values. The HR-1s are better in the big picture to me, but both are quite beautiful with some tuning. The refinement of the HR-1 is hard to describe, and really nice, but the speed of the 944s without crossovers here is really nice too!
If you want to calm down the 944s rather than buying new speakers, you could incrementally mitigate/tighten the bass and mid-bass thickness to taste by plugging the plinth spaces with rubber gasket material or caulk backer foam (as long as these are big enough to seal well when pressed into the space).
Also, if the speakers are feeling a bit in-your-face, you can smooth/soften them a bit...and reduce smearing a little from toning down resonance, especially that causing bass/mid bass muddle. This can be done with Marigo Green 3mm VTS Tuning Dots.
http://marigoaudio.com/tuning-dots/ I got mine direct from the maker, or I think Music Direct had them for $35 for 12 also.
They are cool as you can add one and listen, add another, and so on...and they come off easily when you have added one too many (or if you don't like them). You can even restick them once or twice if you are careful. I think I ended up with 3 on the top mid-bass driver and 2 on the bottom one on my 944s. They musically tightened and speeded up my sound while mellowing edginess (smoother) with no down side. Nice little tools.
The best place for them here was carefully placed on the flat part of the rubber ring where it is glued to the paper driver....between the rolled out rubber part and the paper part of the driver. Carefully placed not to touch the extended/round rubber ring, and not to be on the paper, they fit like they were made for the driver. I used a black sharpie to color them before putting them on, making them look pretty normal.