Peled is playing FLAC files, which means he's looking at improving his 2 channel audio. If he can hear the difference in sound quality between the Hegel DAC and the Burr-Browns DAC in the Yamaha, that means that he's probably using the "Pure Direct" option of the Yamaha to run the audio straight into the pre-amplifer and power-amplifier sections of the Yamaha and completely by-passing any of the digital processing stages. This also means that Peled is one of the few audiophile type people who can hear subtle differences between pieces of equipment.
The Burr-Brown DACS are very popular DACS and they can be good, if used in the proper way. What is probably happening here is that the "audio output buffere stage" between the Burr-Brown DACS and the pre-amp section of the Yamaha is not as good as the audio output buffer stage in the Hegel DAC. The Hegel could also be handling digital timing gitter better than the Yamaha DAC stage. It's impossible to tell, but Peled can hear a difference so there is one.
YPAO won't really help him in this case, since it's mostly targeted at setting up levels of all 5/7 speakers for home theater purposes. The PEQ part of YPAO may improve things here, but then again we are removing the benefit of the Hegel DAC because the Yamaha has to convert the analog audio from the DAC back to digital for YPAO processing, then again to analog to send to the amplifer part of the Yamaha.
In this situation, Peled is correct in looking for a separate power amp to drive the main left/right speakers. However, we are getting into an area of diminishing returns where you have to spend a lot more to get smaller amounts of improvement. Also, there are many different types of power amps and they all have different sound signatures (some that Peled may or may not like). If Peled is after a more natural/realistic sound, I like recommending these Channel Islands amps:
The are 100 watt monoblocks. They use a unique Class-D amp design and have implemented Class D in the proper way (which many others have not). They are a little bit expensive ($1800 US). But you'd have to spend $8k or more to get something that sounds as natural or good. I would not be concerned about the 100 watts as I have seen these amps drive 6' tall Focal towers with 15" woofers without any problem. The JBL speakers are also an efficient speaker, so I would say the amount power is not an issue. The quality of power is what needs to be focused on. You can buy 200 watt Channel Islands, but you're looking at $2500! Sometimes you can find these things used on Audiogon/Ebay, but it's rare.
I have compared these directly to the Pass Labs 2-channel solid states amps ($7k+) and while I would say Pass Labs are about as good as you're going to get with a solid state amp, the Channel Islands just sound more "real" and natural. The Pass sound a little bit harsh compared to the Channel Islands, but compare them to any other SS amp (B&K, Bryston, etc.) and they are still better. I would dare say these would be a significant improvement over the amp section in the Yamaha.