First off, apologies if this isn't the right subreddit to post this in!

I'm currently in quite a dilemma, and am looking for advice. I'm running a small TV station (if you can even call it that) using one of these fancy devices, and a couple antenna amplifiers like these. I have the channel output set to channel 10 on the modulator, and the output antenna going to a big rabbit ears I have, and the input connected to my PC. I am able to pick up the signal on all of my small retro portable tv, as well as a few CRT TV's and a VCR player.

My problem is that I need to pick up the channel on a projector we have mounted to the ceiling, that only has HDMI inputs. I've tried a couple tuners but they don't pick up the channel I need, and our only option besides finding the correct tuner would be to (dangerously) mount one of my heavy VCRs up high and connect that to the projector, or to run RCA cables a few hundred feet to my office, which would be such a pain to do.

My question is, does anyone know of any small converter boxes, or any other contraption we could use to pick up the signal for our projector?