Here is the forum I (admittedly) hijacked with my own issue. The OP had a problem getting external subtitles to run at all.
My issue was in the use of most subtitles at all, and the oddity of using hardware acceleration made a video perform worse than if you did software from the get-go. Well, since you don’t appear to be a pass owner/subscriber, my posts may not be relevant since you cannot use HW transcoding, but take note of the posts by MagaZine. After some back and forth, they mentioned using external VOBSUB subtitles, which should have been direct-played by the person’s player but somehow was causing a transcode. Ultimately, they muxed the subtitle into the file, which helped avoid the transcode.
I’m not sure what your issue is, but it really sounds like external subtitles are just to be avoided. I’m sorry to say that I’m not a fan of them myself, I prefer my video files to be self-contained, so I love the MKV container. If muxing the sub into the file is not acceptable, then I’ll step aside and hope some Plex wizard might know more about external subs - even SRTs - and why it causes buffering.
***Keep in mind that Synology NAS models have weak CPU’s. Even the best option CPU-wise involves a Celeron. Any kind of transcoding will consume the entire CPU. If you are using that for other tasks, then it’s possible your older Sony TV might need a transcode to play a file, which might not be strong enough.
Edit: What model NAS do you have, what is the bitrate of the video, and what is the server version number?