Well. The Aurender is probably as good a source or better than the Moon. I would expect it to perform at least as good as the CD transport... possibly better. I own a Aurrender N150 for my headphone system.
In my main system, I cannot tell the difference between a CD, Stored files, and steaming of exactly the same mastering. That is a good thing, and was the goal. My systems are shown under my ID.. but an Aurender W20SE, and all Audio Research Reference components. There is definitely no good reason the transport should sound better. A transport is a mechanical transport and a streamer combined as you are using it). But it is a little surprising (maybe good) that it doesn’t sound slightly different. Moon (I’ve owned some high tier CD/DAC) is pretty dry and detailed. I would expect the Aurender to be very slightly warmer and more natural.
This does not answer all your questions, however. It is strange that you are not hearing differences between DACs as you switch things around. DACs tend to sound different. Your speakers and amp are pretty sensitive... hmmm.