1) both RCA and balanced outputs to amplfiers ==> Most HT Processors actually have both RCA and XLR outputs. Some of the lower cost or older ones only have RCA.
2) Two RCA and
balanced outputs of Left/Right front speakers ==> The only processor I know that actually has this is the Classe SSP-800. In my opinion, the Classe will be somewhat on the solid-state edge sound in comparison to Bryston/Krell. The Bryston does have L.AUX and R.AUX outputs, but they can only be set to do a stereo down-mix of all the channels. So, you would be getting left/right signals, but also signals from center/surrounds through this. You can do this if you want -- use the L.AUX and R.AUX to supply the servo bass amp, but be aware that it's a "summed" audio signal (not just left/right). If you want true left/right, your best bet is to use a Y-splitter cable (or choose the Classe SSP-800).
3) HDMI ports ==> most HT processors have HDMI nowadays, even previous generation models. But only the newest processors support 4K and Atmos/etc -- if that is a concern for you. I believe the later versions of the Bryston SP3 has one HDMI input that supports 4K.
4) USB ports since I am going to incorporate a Innuos Zenith MK III music server into my system ==> It looks like the SP3 does indeed have a USB port that accepts a digital audio input. This is probably the only HT Processor that supports this. If you find a USB input on any other HT Processor, it is only there for firmware upgrade or remote control codes. You should also realize that you will not be able to support DSD playback in an HT Processor. HT processors are also clocked best support 48khz sampling rate (which most movies are produced in). Any other sampling rates are probably going to be a compromise (but still sound good). If you want a really good music DAC, you should look at an external DAC. Also, if you are not locked into the Innuos, you could look at a different streamer that has digital COAX output (such as AURALiC Aries G1). This allows you more flexibility in choosing a HT Processor.
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In my opinion, the best analog stages in HT Processors belong to either Bryston SP3 or Krell S1200 (1200U / 1200U 3D). Both are the only processors that have fully discrete Class A audio stages (everything else pretty much uses op amps, including Classe SSP-800). Both have benefits and drawbacks. The Bryston SP3 is excellent bass, but mids/upper-mids are too laid back for movies -- it is just not exciting enough and doesn't have enough attack. I think the digital DSP/DAC board in the Bryston is compromised (they use an off-the-shelf DSP/DAC board). The Krell does not suffer from laid back mids/highs and it has incredible resolution, but it can sound somewhat bright/thin stock. The fix is easy - solder some big caps directly onto the rectifier pins for the analog and DAC power supplies. This gives the power supply more capacitance because the Class A audio stages are very demanding. The Krell power supply is undersized, in my opinion. It's basically half the size of the Bryston SP3 main power supply. Also, Krell S1200 does not support 4K.