Ripsaw HD - no video output on PS3 despite DVI-to-HDMI converter

I've been struggling to get video capture from my PS3 since I first got my Ripsaw (Wii U, Switch, and PS4 all doing just great, though!). After a lot of googling and some additional hardware purchases, I can now reliably get audio to work seemingly universally, and for video to come through to Streamlabs in SOME circumstances, but not others, and it's driving me up the wall because I can't figure out what's wrong this time.

For the sake of thoroughness, my hardware/connection set-up is:
PS3 ("fat", not slim, if that matters) HDMI output --> DVI input of (Monoprice brand) Converter box
Converter box HDMI output --> HDMI input of Razer Ripsaw HD
Razer Ripsaw HDMI output --> HDMI input of TV
Razer Ripsaw USB output --> USB input of PC, on which I've been using Streamlabs OBS for recording/streaming
(I also have the audio running through the Converter box via SPDIF, which seems to be working perfectly, so I'm not concerned about it.)

My assumption is that it has SOMETHING to do with whether the video output is 1080p or not.

I'm getting a little frustrated, honestly, because the ONE game that was the main reason for my getting a recording device happens to be a PS3 game that runs at 1080i. Is there ANY way to fix this? A setting I've missed? A different piece of hardware? Please help.