If you stop using the inbuild DAC of your amp you will find yourself with a better amp. I would stay away from NAD CS1 without a listen. A cheap option would be to get a Cambridge Audio DAC Magic and connect it to your tablet with a USB cable. You can control playback with a smartphone/PC when using Tidal and Spotify, I don't know about other services.Sounds interesting, do you what it's model name is etc?
I've decided I'm not in a hurry. I'm fighting the mistaken need to upgrade my amp too. I've got Roon streaming through the Connect into the amps built in dac and it sounds perfectly good with a bit of room correction.
EDIT: It's a NAD CS1. Has an onboard DAC, and SPDIF coax and optical out. No app, so no bluesound, it's operated from the native apps, and is Roon ready. So you can stream directly from the Tidal or Spotify apps, and use Roon or something like Bubble for Qobuz. It's still £300 though, that's £280 more than the used Connect I'm using.