Best bang for buck integrated amp for $500

The Triangle Bro 3 responds well to both class D and class AB. There are alot of class D amps coming out of China under $500 and some match up with their respective dacs. For class AB, buying used, an NAD or the Rega IO are also choices.
When I was looking for a small form factor class AB amp I came across the Keces E40 which was reviewed by Soundnews, so you can look up his take. I concur with his findings. The Keces E40 is slightly more powerful, has the same connections as the IO and adds a usb dac (not that important to me) but also a pre out for a sub or amp connection.
Compared to other amps I have tried, including an Emotiva A400z, it hands down sounded better. The emotiva added more wispy highs but the lows, mids and highs of the Keces are full bodied , and well fleshed out, and has better depth and separation. Bass and mid bass are tight. Made in Taiwan, not the ROC if that’s important. And has great looks. Unfortunately, it is a bit over your $500 budget at $630.
I havn’t heard the IO but it is also well regarded for $600.

But, the Triangle Bros will sound great on class D amps as well. I have the Focal 807w and Triangle Zetas. My cheaper class D didn’t bring the best in the Focals but the Keces sounds as good on the Focals as my Hegel. In fact it sounds alot like it at low to moderate volumes which is where I listen. 

Class D and class AB sound great on the Triangles. But the Keces makes them sound better for me but I could easily go with class D on them. Not so with the Focals, they need the punch of a solid class D.Anyone else hear the Keces e40?... let us know your thoughts.

I wondered how the Rega IO would compare to the Keces E40 I have. Essentially the Keces outputs similar watts but a measurement I found showed at a fairly nice distortion curve. It is also stated to be able to output up to 15 amps which if true shows some decent design.
I find its’ bass output substantial, tight and fairly layered. The stage depth isn’t flat, there some dimensional to it. I think you stated the dac wasn’t up to par and I cannot attest to that however one reviewer found it quite capable and competitive as to audio quality even though it doesn’t do more than cd quality. Same with the phono stage, ancillary but capable. Plus, it has a pre out.
The sound quality is what I was apprehensive about because there are no returns on the purchase. But the Soundnews review was IMO, accurate. It doesn’t quite give those wispy, super airy highs but the highs that are produced are musical and have body/weight to them.

The tonality reminds me of my Hegel h160 to the point that if I were to AB test both amps for someone not familiar with them, they probably couldn’t tell the difference.

Still, someone will eventually do a comparison of these smaller amps. If you listen at moderate volumes, you may find you’ve found a unicorn.

I've carefully read and re-read your posts regarding your experience with the IO.  Not sure, but doesn't bass need a bit of room to fully spread out?  If your up close to the speakers as in a desktop setup, it might sound like less bass than if you are further away.  The upper mids and highs might be grabbing your attention more than the bass, perhaps?
The reviews from alpha-audio.net state this about both the E40 and the Io:
Keces E40: What immediately strikes you is the exceptional low-end that this amplifier sends through our speaker. We have seldom heard so much power and control from such a small box. The Rega Brio is the closest but the Keces E40 goes far beyond… Bizarre. A lot of modern monitors can use a kick in the butt, but of course it’s important to keep an eye on them. With our little Cabasse Surf mini-monitors it was sometimes too much of a good thing. 
Rega IO: Coincidentally, we ourselves have a fine, modest amplifier in our listening room! It’s the Keces E40 (599 euros) which, as its name suggests, has 40 watts in class A / B on board and also performs a bit above its level. It even delivers some decent watts in pure class A. And it offers, besides a phono stage, also a USB dac. So there are more similarities than differences between both amplifiers. But in terms of sound we notice some nuances here and there. The io has a more powerful bass and is a bit more playful than the Keces. The Keces is a bit more balanced to our feeling but a bit less transparent. Choices, choices, choices. 
I know how most of us feel about reviews, alpha audio says the Keces e40 goes beyond the Brio but says the IO has more bass than the Keces but suggests it's less than the Brio?  Kind of doesn't make sense.
The Keces has some kick like no other amp I've tried under a grand has but it's also smooth. I think the IO adds a bit to the upper mids and treble which if not balanced with the lower mids and bass will stand out to much so all you'll focus on is the brightness/clarity at the expense of bass (SoundArtisit SA-200A did that, way too bright in my system).
Are you jumping the gun selling off the equipment too soon because you are frustrated?  I might have jumped on the Triangles but I have the Zetas which have a titanium tweeter.  Not sure about the softdome.
As to the amp, I am very tempted.  It may give a bit more aire on the upper mids and treble but if the energy is too much, it might overshadow the lows. The Keces doesn't have quite the aire of the Emotiva A400z which was way more powerful than the BasX A100 but I liked the high frequency extenstion, but overall it didn't sound like a higher end product. The lows were a bit less, less defined and overall the SS was very 2 dimensional.
Maybe your jumping the gun.  Give it time for your brain to adjust too.  Unless you just hate your system, keeping it intact will allow you focus on what you like or need and when you do get something else, the comparisons will be more useful when you swap equipment in and out. 

Something to think about as I know how frustrating one can get from experience regarding audio.

I took a look at the Burson Funk and if one needed an amp for primarily headphones but wanted speaker capability it could be a good option. 45/35 watts at 4/8 ohms respectively, while my amp is about 60/35 watts for speakers but hasn’t the output for headsets as the Burson. It does add preouts and a MM input, as well as a basic USB, plus two RCA inputs for less.

The Burson took a price hike to 799? A review stated priced from $544, that’s quite a recent hike unless I’m missing something?