There are plenty of old MIDI interfaces that have MIDI clock to SMPTE (and vice versa) conversion and standalone modes. I’m pretty sure the old Midiman MidiSport 8x8s I picked up recently for next to nothing will do it in standalone mode, and I think the older MOTU Midi Express interfaces from the late 90s-mid 2000s (at least the two bigger ones) will do it, too. I’ve never actually tried it myself, though. There are also a lot of little boxes from the 80s that will convert Midi time code to SMPTE and vice versa and those are usually really cheap, like under $10, but they’re cheap because they don’t handle Midi clock (which didn’t exist yet), just MTC, so they’re useless with most modern gear that only does Midi clock, unfortunately…
Actually, I happen to have a friend’s old MOTU Micro Express half rack MIDI interface on loan right now, and I just confirmed it has SMPTE i/o, but I have no idea if it will convert between SMPTE and MIDI clock in standalone mode. If it does, they’re pretty cheap used and not too bulky (1u half rack and about 5" deep). That would be a pretty good option plus you’d get a halfway decent MIDI router/interface, too. MIDI clock out from the OT into the MOTU, SMPTE out from the MOTU to the video people and MIDI out from the MOTU to your other gear if you use any. Also it would give you the option of actually slaving the OT to video instead of vice versa, if you felt like it. Just make sure to find a manual and confirm that it will work in standalone mode before you buy one. And steer clear of the current version, AFAIK the MIDI timing is better than the old ones, but I’m pretty sure they dropped the SMPTE features. You want the old one that looks like this:
I just checked eBay and there’s one for $34 USD right now.
There was an even earlier version that predates USB and has a serial port on the back. It might work too and would probably be even cheaper but I don’t know much about that one.
Again, though, I haven’t actually used the SMPTE features on any of these so I don’t know for sure if it will convert MIDI clock to SMPTE in real time or if it has to be the master clock or what, so check the manual online to make sure it actually works if you’re thinking about going this route!