News! I found a recommendation to try setting the NAA buffer time to 10ms from here: HQP and Chord Qutest - Audio Gear Talk / HQ Player - Roon Labs Community and I am happy to report that using this, the clicks, pops and white noise are hugely reduced when I play HQP into the usb input of the qutest.
I have been testing much of yesterday and today with the usb into my qutest, playing 44.1 upsampled to 705.6 and 48/96 upsampled to 768 and I have had very few clicks (they may have been on the recording or the fridge turning on as well) and only one tiny burst of white noise yesterday at 768. I tried increasing the buffer time to 20ms and this resulted in more clicks and white noise so I am currently trying reducing the buffer length to 5ms. I don’t recall any white noise today. If there are still clicks, they are very few and not noticeable. Whatever the case, the situation is much much improved using this buffer time setting.
This is transformative! I have no idea why it works (I always thought more buffer was better) but I am not questioning it. It really does sound very good now - nice and 3D and with lots of things going on in the stereo image. I am well pleased with this and I hope this write up helps someone else with the same setup.