If it’s what it sounds like, that game uses 240p for gameplay and 480i for menus; and, when the video mode changes, sync drops briefly. On CRTs, the displays with which the Saturn was expected to be used, video modes can change very quickly, so switching between the two modes frequently can be done without inconveniencing the player.
Unfortunately, when sync drops over an HDMI interface, all of the HDMI devices between the source (the OSSC in this case) and the display need to reestablish sync, and it usually takes a second or two for everything to come back. From what I’ve seen, games for HDMI consoles tend to output at a single resolution for everything, so players won’t be inconvenienced with the time it takes to recover from a mode switch/sync drop.
Unfortunately, there isn’t much you can do–even the Framemeister isn’t immune. The only device I’m aware of that can make those video modes seamless is a presentation switcher, which will maintain a consistent resolution and framerate on the output regardless of input or lack thereof, but at the cost of dropped/inserted frames (which cause video judder) and added lag from the scaler. Analog presentation switchers are affordable, but will not handle 240p properly; and I’m assuming HDMI presentation switchers are recent enough that they’re significantly expensive.