It's probably nothing to do with the AVRs DAC - it is almost certainly good enough. It's the AVR amps that will at best lower tier 'cos there's so many of them.
For example the Rega io £400 is a very good and pretty much the cheapest budget stereo amp. Your SR6013 has 9 amps. 9X £400 /2 = £1800 just for the amps, then there's the cost of all the processing - so lets say about £500 covers the preamp the DAC loads of sockets etc.
RRP of SR6013 is £1299 so less £500 = £800 for amps or less than £90 per amp
A decent budget basic amp is say £300 a channel, midrange £500 etc And the amp
@gibbsy uses is about £800 a channel.
There's a way round this using an extra good quality stereo amp.
The AVR
needs pre-out and stereo amp
needs a HT Bypass function or a full tape loop.
Connect the music sources into the extra stereo amp, the AV sources into the AVR.
Connect the L&R front speakers to the stereo amp and the AVR L&R pre-out to the HT bypass on the stereo amp.
Et Voila ! Music through the stereo amp but also in AV L&R still driven by stereo sound.