Ixnay on the frustrating!!! 
With that said, get yourself a Harmony hub (EDIT: I didn't see RF and the Harmony Hub doesn't do RF). Or, alternately, the Broadlink hub. I don't know how well it works, but it had gotten some good reviews. The Harmony Hub would be my first choice if price isn't an issue.
There's also the Sonoff RF which is good, but you'd need to flash it with Tasmota or the Sonoff firmware here in the forums to make it work with HE.
I don't see any mention of the frequency.
If it's 315mhz or 433mhz and can be intercepted by the RC-Switch library I've got the Particle Photon setup for you!
If not... It's probably a rabbit hole I've not been down...
I believe @bptworld has something put together for IR, but it can probably just use a different module for RF. Can't find his thread on it though. Can you help Bryan?
That's the Sonoff firmware I was looking for! Thanks!
Check input voltage of your projector motor and ditch this remote and use a Zwave shutter module:
Interesting product. So one way you could do it is with Google Assistant Relay. With that you can send silent commands via Google Assistant to control it. Depending on what kind of control you get through Google Assistant, you could control this with RM.
It would be cloud based (two of them actually), but then the Harmony hub requires a cloud connection under normal conditions, so this isn't much different and it's a lot less expensive (albeit, a lot less feature rich too).
I have a Harmony Hub, but I thought it was limited to IR and not RF. Guess I need to do some more reading.
I actually have mine blocked at my firewall. I only allow it outside access when I need to update it or change an activity or device (which is rare).
I was thinking about picking up one of the Broadcom devices just to see if I could get it working in HE.
Crap. Belay that. The Harmony Hub doesn't do RF. I could have sworn you said IR and not RF. I'm sorry about that (it was late lol).
But, you should get a Harmony Hub anyway because they are simply cool devices. 
I believe its 868mhz (or close). I think thats what it said on the back of the remote, but I don't have it in front of me right now
Yeah, they can do Bluetooth, IR and WiFi (Sonos).
Brain fart on my end. 
Good suggestion, Will look into it.
How does it still work? When mine is offline, it doesn't work.
Are those two individual relay contacts, plus a motor control, or is it a single, double-pole relay, plus motor control?
Manual says the motor is 110 VAC, 60HZ.
And the remote receiver is 230V / 50hz,
https://fccid.io/ZKA-1GD-868MN/User-Manual/Users-Manual-1471503.pdf
Offline and blocked are two different things. It's still "online" on my local network. It just can't reach out to Harmony's servers without my permission.
I do the same thing with my Echo devices. I don't allow them to update stats back to Amazon:
2019-03-19 10:33:06 A device-metrics-us.amazon.com alexa-guest-bedroom-echo.lan Blocked (gravity)
Interesting. What do you block? E.g. How can I do this too?
Download the Hubitat app
