Ethernet cable for music streaming

I know there have been threads on this topic, including my own from last year, but I'd like to pursue this issue further, perhaps from a slightly different angle. Here's my conundrum: I'm not getting the sound quality from my Innuos PulseMini streamer that I think it's capable of and I've never been able to put my finger on what the weak link in my system is. I'm streaming Qobuz through the Innuos SenseApp on my Samsung tablet. While some parts of the frequency range sound really good (bass, mid-bass, lower mids, e.g.), when we get to the range where vocals live and above, the sound loses fidelity and definition. Things sound fuzzy and muddled, especially if the music is complex or dense. Loud orchestral passages can be really unpleasant to listen to.

The streamer is connected via USB to a Sonnet Morpheus DAC, and is fed via ethernet cable from my AT&T router. It's about a 35 ft. run of CAT5 that goes under the house and up through the floor of my listening (living) room. It doesn't run near any other electric lines. There's an ethernet switch that divides the signal between the TV, the Roku box, and the streamer. I do have the option of running a dedicated line from the router to the streamer, but I need some advice on whether this will improve things any. I tried plugging the existing ethernet cable into the streamer directly, bypassing the switch, but this yielded no improvement. 

Would it help to use CAT6 or CAT6a cable for this run? And should it be shielded or unshielded? I've read some posts that indicate shielded cables introduce their own distortions into the signal, so I'm really not sure which way to go here. 

I'd be grateful for advice from the many of you who are more expert on this subject than I am. Thanks.