I have a script working with youtube-dl that (cautiously optimistic) appears to solve the problem in initial tests. I need it to bake for a few days to be sure, but things seem to be working correct-ish now. Thank you so much, canuckInOR!

There was an interesting technical snag with it that I'll recount here for fun:

Youtube-dl needs ffmpeg. It calls out to ffmpeg to get some of its work done. What's really interesting is that youtube-dl doesn't actually download the data itself and then feed it to ffmpeg, no, it actually shells out to ffmpeg to get the downloading done too, once it's worked out the actual final URL with all the doodads and geegaws added in.

That's fine though, because the Synology distro already has ffmpeg installed for its video transcoding functions.

But there's a problem. The version of ffmpeg that's installed/running in the Synology distro doesn't work properly with youtube-dl. The youtube-dl program seems to start up OK and do its initial work, but then it tries to launch ffmpeg, which then displays an error message saying that it can't download from HTTPS sites and that I have to recompile it if I want that. (Of course, since the Synology uses ffmpeg for its transcoding I can't be recompiling it willy nilly.)

I can't just change the URL to HTTP instead of HTTPS, because I tried that, and after the youtube-dl processing where the URL doodads and geegaws get put in there, it changes it to HTTPS anyway.

Fine, I say, I'll just use the "--hls-prefer-native" or the "--external-downloader wget" parameters to youtube-dl. Either one of those should have solved the problem. NOPE! Those parameters actually don't work at all and have no effect in the current version of youtube-dl. I put the parameters in there, but ffmpeg still tries to download the video and still gives me the error message saying it can't download HTTPS. I will someday file a bug against youtube-dl once I can gather all the necessary logs and stuff, but they're like 2200+ bugs deep at the moment, and I don't expect they'll ever get round to fixing it at this rate.

Last ditch effort: Use this youtube-dl parameter: "-g, --get-url Simulate, quiet but print URL". This works to get me the final URL with all the doodads and geegaws added. Which I then farm out to wget myself.

This seemed to work, but looking closely at what got downloaded, I see that it doesn't actually start downloading real video. It just downloads a text file which catalogs additional URLs to sections of the video stream.

Before I went any further, I just thought, you know what? Let's just see if that alone, is enough to keep the stream alive. And left it that way.

So far? Seems to work. Crossing my fingers.

Thanks again!
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Tony Fabris