You didn't state what service you use for streaming. But BT is about the worst quality you can get. Your TT & Cart are good, so invest in the streaming side.
If you use Tida/Qobuz make sure you streamer will support it natively, meaning it will stream from the streamer, and your phone will just mirror/control the streamer.
$2k will get you a nice streamer, with your other gear, think Cambridge Audio will sound very good. My system has Forte II's with a CA streamer it sounds just as good as my TT.