I am thinking about picking up a shield as a client in a similar setup. If you're using subtitles -- does the shield handle them well? That's the part that keeps breaking in the native TV client.
I use Kodi with the jellyfin plugins on my shield and it works well. Subtitle support is pretty good but occasionally I need to restart the app to get new subs to display for a show.
The native jellyfin client is ok for simple things but it's far more limited than Kodi.
The subtitles I use are most often ones in separate files alongside the video files, named appropriately for the jellyfin server to see it. I think embedded subs work well too, sometimes needing burning in, but my server can handle transcoding.
There are some quirks with using Jellyfin+Kodi with external subs. It used to be solved by the "direct play" feature in Jellyfin4Kodi where it would just pass Kodi a link to the SMB/NFS shares, but the newest releases of Jellyfin have deprecated and hidden the server side feature that enabled that. I had a talk with the devs about it on GitHub and they don't really know if/when it's gonna come back.
The Shield uses the same Jellyfin client as any AndroidTV/GoogleTV box. You can use Kodi on the Shield if you want native support for more subtitle formats, but that's also true of other AndroidTV/GoogleTV devices.
