I'm running a DMP-A8 in my living room/TV system and a DMP-A10 in my dedicated system. Before I got the streamers I used an ASUS gaming laptop for streaming Qobuz.
My main advice is to use a control as you attempt to detect sound quality differences in streamers, or DACs for that matter. I have a pretty high end CD rig (Jay's CD3 MK III Transport and Berkeley Reference Series II MQA DAC) and I have compared the streamed content from Qobuz to the corresponding CD (make sure they are the same version) and I can't hear the difference between a CD and Qobuz streamed on my ASUS gaming laptop (hooked up to the Berkeley through the Alpha USB). If you believe the hype, the computer should sound awful compared to CD played through the same DAC. I'm pretty sure that even a trained listener couldn't tell the differnce in a blind test.
I seriously doubt you will hear a difference between the BAT DAC and the DAC in the Eversolo. But if you buy the DAC first you can hook up the Eversolo to the BAT and bypass the built in DAC. Then you will be able to compare the two DACs over a period of time.
When you hook up a new expensive component the angels always sing. But if you compare it with a standard over a period of weeks or months I think you will come to the conclusion that the sound is very similar, if not identical.
As mentioned above, I'm running a DMP-A8 in my living room TV system and I have a DMP-A10 in my dedicated high end system. I have compared the DAC in the A10 with my Berkeley and they sound so close that the differences, if any, are insignificant. I typically run the A10 using it's own DAC - it's just easier that way.
Using the Eversolo I run the Eversolo app that duplicates the screen on my phone which works fine for me. I only have Qobuz for streaming. And I'm a total sucker for those meters.

