If you’re set on an Android Operating System, then NVIDIA Shield is probably your best bet. It will offer Gigabit ethernet connectivity. However, this assumes that the limiting factor causing your playback pauses is, in fact, the ethernet connection. Another possibility is the speed of the PC or NAS device reading the media from wherever it is stored. Actual read speeds vary greatly depending on the particular hardware.
The fastest way to know if a stand-alone streaming box will fix your stuttering is to try one. Just make sure wherever you buy it from allows trouble-free returns. If you try an NVIDIA Shield and it doesn’t fix your stuttering, just return it. You may have already viewed this post, but in case you haven’t, the following is a good read for all things 4K via Plex.: Plex, 4k, transcoding, and you - aka the rules of 4k - a FAQ
