The cheap upscaler probably frameconverts every input type to a standard framerate (as well as interpreting 240p input as 480i from the beginning), so the display does not drop image.
3-4 seconds sounds unusually long though, in my experience OSSC resyncs between interlaced and progressive modes should not take more than half a second or so. The main culprit of delay is more likely your screen.
It could be that transitions take less time if you have your 240p mode and 480i mode set to the same output, ie. Lx2 240p to 480p and bob-deinterlace 480i to 480p. However, the framerate still changes slightly so your display will still drop the picture for a moment.