Most slowness comes from exit nodes which you don't need to access onion services. There're also single-hop onion services, which should be a bit faster while sacrificing server anonymity if i understand correctly

Is there a safe service I can try out to see how fast it can potentially be?

Depends on your definition of "safe", but there's an official Onion service for Facebook for example: http://facebookcorewwwi.onion

You can watch videos on it fine these days - though I wouldn't recommend, for social ethical reasons, using it for streaming movies/music off your personal server.

Unless of course, you are running a node.

It is. It's not practical for this use-case.

It’s slow, with NSA hunting at exit nodes.

Exit nodes aren't used if one connects to an onion service.

And for all we know, the NSA snoops traffic at all major internet exchanges, so tor exit nodes might get extra attention, but so do e.g. people who's search history suggests they might be sysadmins (if i remember reports on xkeyscore selector correctly)