That's to be expected, your AV receiver's processing will cause a delay. Bear in mind that many large clubs/arena setups etc will often have a similar delay effect, which is why DJs have booth speakers close by (and is usually little or no delay).
There is no delay setting in Rekordbox that'll do what you want. Software such as Rekorbox strives to always limit latency.
You could use bluetooth headphones - but there's no guarantee that the delay on the headphones will match the delay coming through your speakers. You'll also have the issue that your actions on the controller (play, cue, hotcue, etc) won't match what you can hear in the headphones... and that'll be WAY more off putting when trying to mix.
When setting your receiver to stereo direct, you bypass all the processing, so your audio isn't separated from the two channels (front left, front right) that is supplied to the multi channel set up you have.
Since you're saying that the audio isn't great on stereo direct, I'm guessing you only have satellite speakers. If the delay is a problem perhaps look at full range speakers.
I don't use my AV receiver and HT speaker set up (I've also got a hefty Atmos setup) for DJing, studio monitors/PA speakers are better suited. But if I wanted to, I'd set my receiver to pure audio/stereo direct and would be very happy with the sound the front speakers produce (subwoofer often doesn't kick in due to the bass capabilities of those speakers).
So your options are:
- learn to live with it;
- buy bluetooth headphones but suffer delay between your actions and what you can hear when cueing;
- buy speakers to use in your "booth", but then others listening may also hear the booth output;
- replace your front HT speakers with full range speakers;
- find an alternative AV receiver with lower processing latency (expensive).