What is the best sounding Pre/Pro 7.1 channel with analog bypass.

I agree with big_greg.  Finding a good sounding processor WITH HDMI for $500 used is going to be very hard.  There's an Anthem D1 that has been upgraded with HDMI on audiogon for $670.  That's likely to be 15 years old.  The Integra DTC-9.8 that big_greg recommends can also be 12 or so years old.  

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for something newer, there's actually a Integra DHC-60.5 on ebay for $350 plus $99 shipping.  They say "barely used", but I wouldn't believe that too much.  But it's cheap and originally retailed for around $1600. 

What about a new Outlaw Model 975 prepro since you're already running their amp?  Only $550. 

https://outlawaudio.com/products/975.html

Actually, that's a pretty good suggestion, if you want a new product.  The Outlaw 975 is very well designed and laid out as far as internal architecture goes.  It runs in the same league as the Emotiva UMC-200 did.  If you were looking at a new product, I would actually suggest the 976 model instead (for $929, which is well within your budget for "new").  It supports balanced XLR outputs and has much better power supply and power supply filtering - plus it supports HDMI 4K for future.
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That being said, I still think that Integra DHC-60.5 would be a better choice.  It has much larger power supply and much better components than the Outlaw (capacitors, transformers, etc.).  It is used, but you would get better sound quality in the end.  The Outlaw is built based on very similar principles to Emotiva -- to build the best design as possible using the cheapest components and sell direct to customer (no retail distribution) to give the best "bang for the buck" for the consumer.  They definitely succeed in that.  But keep in mind that Integra originally retailed for $2k (I just checked) and was highly mass marketed and distributed (which means it's still cheaper for a given performance that the boutique companies such as Bryston or Krell).  Integra DHC-60.5 comes in at 24lbs, where the Outlaw 975 is only 9lbs, the 976 is 12 lbs.

If sound quality is paramount, I agree it's better to find something used if you don't need the latest, greatest features.  Personally, I'd try to negotiate this Anthem AVM40, then stick a crowbar in my wallet and just buy it as long as it meets your needs.  Retailed for $3700 new. 

https://www.ebay.com/itm/192894634996?ul_ref=http%253A%252F%252Frover.ebay.com%252Frover%252F1%252F7...

Interesting suggestion.  The AVM 40 is likely a very excellent contender for sound quality, however it's missing one critical element that would be a deal-breaker in my mind --- the ability to support the new bluray audio formats (DTS-MD and Dolby True HD).  It is also older than the Integra by about 5-8 years.  Kind of like buying an old Krell HTS or Showcase processor.