I actually tried the SP3 in my system. Before I speak, you should probably know that I am extremely highly critical of equipment and sound - to the point where others say that I'm splitting hairs, lol. A sound extremest, if you will.
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That being said, I tried working with the SP3 a lot. It definitely had very good sound quality, probably the best bass I ever heard from a processor, but the sound was just too laid back for me. I could hear that the Class A audio stages were very good, but I just did not get enough attack / slam / detail in the mids and upper mids for my tastes. Also, I don't think I was getting good resolution output. I believe the Digital/DAC board is compromised in the SP3 because they use an off-the-shelf digital board from Momentum Technologies. So, I think the sound will not be quite as clean as other processors. With all that, it could be that you would like the SP3 just fine. It has a big following over on Audio Circle and AudioAficianado forums and many people rave about the SP3.
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Ultimately, my older Krell HTS 7.1 was highly superior in sound quality, but was very old. After trying multiple processors, I run with a Krell S1200U, which is just about the best sound quality processor in my opinion. However, it is just a little older and doesn't support 4K.
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Because of your 4K requirement, it is going to be difficult to find a good processor in your budget. I think the only thing I would recommend is to go get a previous generation Marantz AV8802a. They are readily available "new-in-box" from ebay and sellers such as Crutchfield at the $2500 level. They are excellent sound quality, has very large main power supply and excellent local power supply capacitors on the DAC I/V board, and also has fully discrete analog output stages. The Marantz has excellent sound quality, but is voiced to be warm sounding. The upgrade the fuse to something like Hi-Fi Tuning Supreme or Silverstar to reduce the "warmth" and increase the clarity/detail. I think that's about the best you can do.
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I tested the latest Marantz AV8805 in my system and was quite impressed. It had very good slam and impact, but my Krell S1200U just beat it on high frequency clarity and detail (something that can be easily fixed by fuse upgrade).
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Like I said before, probably the first thing you can do is to buy a multi-channel amp and connect it to your Denon receiver using the Denon "pre-outs". That would give you a big jump in ability to let your B&W speakers shine! Then you can always replace the Denon with an HT Processor in the future (with additional amps for the remaining channels if you need them). Many amps will have a 12V remote turn on trigger, so the only thing you need to do is click the "power" button on the HT Processor remote and all your amps will turn on automatically (so it will almost be like using a receiver).
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Or you can get HT Processor and amp(s) at the same time.