Could you try Line4x mode? It outputs 960p for both 240p and 480i, so this should take the monitor’s slow sync speed out of the equation.
Careful—although it outputs 960p for both modes, the input (and hence output) frame rate is still different between the two modes (59.82 Hz for 240p source, 59.94 Hz for 480i source). So the monitor will still have to re-sync.
The real solution is to get a secondary processor that can handle these transitions well. The XPC-4 is one of the best (it handles these transitions in about a second, usually less), and its DVI input makes it a great match for the OSSC’s DVI output, but at around $400 it’s not a practical solution for most. Unless you also are interested in being able to render the 960p image at native resolution inside a 1080p window—which the XPC-4 also does flawlessly—or output in VGA/component/S-video/composite, which it also offers.