I did try a few different things, and I found that the linetriple is a fair bit more stable when I run the signal through my AV receiver (a Denon AVR-S910W), though still not what I would call playable for anything action-based. Changing the HDMI Tx mode has no effect at all, and the sync drops are definitely on the digital side of the equation, as I’ve kept an eye on the OSSC during the drops and there’s never so much as a flicker of red from the LEDs. Normal linedouble works fine, which would also rule out an analog sync issue.
I’ve switched off all the postprocessing features on the TV and AVR and switched them into their respective gaming low-latency modes, but I don’t have a CRT handy to get a good measure of how much lag may still be introduced by the chain. Experimenting with some of the pair’s processing features seemed to improve stability in some cases but worsen it in others, so I ultimately chalked up any improvement to the TV’s handling of the OSSC’s out-of-spec signal just being unpredictable.