"My room is about 20 x 30 with a high ceiling."
Aha! The good news is, your problem is identified. The bad news: upgrading your CDP isn't going take care of it. But no wonder you're here asking about ways to improve the sound.
Actually, the problem isn't your room -- that must be a great room. (Literally!) And it isn't the speakers, those are very good speakers. In fact, I'm not going to be so simplistic as to say the problem was the combination of the two, even though that's true.
The real problem lies (and I use that word advisedly) with the salesman who sold you that gear for that room. Either he neglected to ask the right questions that would have told him your needs, or he knew what he was getting you into, but chose instead to make an easier sale by catering to your stated budget and/or desire for compact gear (and, most likely, whatever brands/models you walked into the store positively-disposed toward from reviews and advertising). Either way he didn't earn his commission -- more like he saw you coming from jump street and pilfered it.
Anyway, this is where you are now: the 1.6's absolutely require a subwoofer to give anything like realistic response in your room. Which is not to say that adding one will cure everything you're hoing for, or that spending the same money (1.6's + sub) on a different pair of speakers (and not Thiels, fine as they are, or not new ones anyway) might not have been a better buy. But it's just the laws of physics which dictate that a pair of 6" woofer/mids -- even excellent ones with 3" voice-coils -- operating in cabinets with probably around 1.5 cubic feet of volume won't be adequate to drive circa 5,400-6,000 cubic feet of listening space (assuming a mere 9'-10' ceiling height, since you didn't specify other than to say "high") as the frequency descends.
And unlike some other small and small-woofered floorstanders or monitors, the 1.6, being a Thiel, doesn't have a shelved-down tweeter and a mid-bass hump to distract you from that reality (although to me the tweeter in the 1.6 doesn't sound quite as extended or detailed as those found in more costly Thiels, perhaps a wise and deliberate choice for this model). These are speakers that can sound great -- albeit still not with big balls in the low bass -- in rooms up to around 1,750 cubic ft. or so (example at the larger end of that scale: 12' x 18' x 8'). You can see the imperative -- since your room is at least 3X that volume, you should be having at least 3X the speaker in it.
Or use a subwoofer. I've actually auditioned the 1.6's in a room not far from the size of yours (in other words too big for the speakers), with and without a sub, and adding the sub can really help a lot. The one I heard them with was a smaller REL, but I'm not sure which model.
Steveaudio is probably right on target with this recommendation, for the reason that REL subs are designed to work strictly in "augmentation" mode, meaning they don't cross-over to the main speakers but simply add their LF response to them. The downside to this strategy is that it doesn't increase the volume level your small speakers can comfortably play at in a large room, so if you like to listen loud the 1.6's may still limit you in this area. The upside is that by augmenting rather than dividing the LF region between the sub and the mains, it will be much less difficult to get an acceptable transition between the two, because in your situation the 1.6's will need reinforcement in more than just the bottom 2 octaves.
By running a sub like an REL, which overlaps the mains through the mid-bass and *subtly* continues into the upper bass/lower midrange, dependent on how you set the contols and subject to adjustment with different recordings, you'll be able to add not just extension but also some of the warmer tonal balance that you are looking for. This won't be without some compromises -- for instance, it would easy to mess up stuff like male vocals or acoustic piano this way if abused, and certain aspects of reproduction will probably be a bit less natural no matter how judiciously the sub is adjusted because of how much you'll be asking it to do in this case -- but the advantages will almost certainly outweigh the disadvantages by a useful margin if done right. The only other caveat I can see is that a sub with a remote control might be most welcome in your situation, but I'm not sure which companies offer that. (Again, I think the Thiel sub would probably be outstanding for you, but don't think it makes as much sense in your situation unless you were upgrading the speakers -- to bigger Thiels in specific -- as well, though you could always take the incremental approach.)
However, I will disagree with Steveaudio about priorities. To me -- and I say this as a Thiel owner, who has gone from mass-market to mid-fi to high-end digital in my time with them -- you're probably better off getting the sub first if you're going to keep these speakers and continue using them in this room. I don't have any experience with your particular CDP, but most of the mass-market players from the past 15 years that I have heard tend to err on the 'warmer' side in terms of overall tonal balance, even if their treble presentation is not refined in and of itself, and their low bass may lack extension, control and dynamics.
In other words, when you do upgrade your Onkyo, don't be too surprised if you find out that it wasn't significantly thinning-out the balance, as much as perhaps doing things like flattening the soundstage, diminishing tonal and dynamic contrasts, glossing over fine detail, lacking extension at the frequency extremes, and giving a less defined, more amorphous presentation. And I'd say to save gear racks for last, if at all, since it sounds like you've got your stuff on a stable base, and besides which that whole topic is small potatoes compared to what your main necessity is at the moment. But my take is that you won't enjoy a new CDP nearly as much until you address the subwoofer first.
One more thing: I suspect you still may need to play around with set-up, sub or no sub. With the speakers 12' away and 12' apart, I imagine they're on the 20' (short) wall, firing down the 30' length of the room, and probably at least somewhat angled-in toward your ears? And that you don't have any acoustic surface treatments or stand-up damping devices? Please let us know about this, as well as your ceiling (height and construction), and how damped the room is in general (rugs? wall hangings? lots of furniture? or not -- lots of windows? much bare floor? concrete or brick anywhere?), and how far away from the wall your speakers are -- maybe further tuning is in order.
