I would definitely look at Denon, Marantz and Pioneer Elite in the $ 1k range before concluding that Onkyo owns this segment of the market. I bought a used Elite that doesn't have HDMI from an AGoner recently because I valued it's "i-link". It sounds great but Pioneer has changed to Class D amplification in it's latest AVRs so that is an issue. The AVR that
Preceded the Pioneer was a Denon In the $1k range ( I gave it to my daughter and still enjoy listening to it when I am at her place. It has a more in your face sound than Onkyo that works better with movies and some types of music.
For $3k I would be considering a separate prepro and amp. Marantz and Parasound would be my idea of a good pairing.