Speaking purely as a guy who cleans and converts VHS to digital for a living, I’d personally just use the passthrough mode with the majority of PS2 games. The reason the 2X, 3X and 4X modes look so good on Sega Mega Drive, SNES and N64 is because the majority of the games output at 240p or 288p. Because the signals are progressive, that means the OSSC has all the lines that make up the frame right from the word go. The PS2 on the other hand primarily outputs at 480i or 576i – interlaced video signals. What that means is the console alternates between showing the odd and even numbered lines that make up the frame separately. In progressive video, 30 frames per second is just that. But in interlaced, 30 frames per second is actually 60 half-frames per second. Not half as in chopped in half, but half the lines that make up the frame. That means with 480i or 576i content, at any given time the OSSC only has half the image to work with. Linedoubling such content means half the vertical resolution is lost.
For that reason, I would NEVER linedouble an interlaced signal unless it was a re-release of an old 288p game that was converted to 576i. The PS2 has a few games like that, such as the Sonic the Hedgehog collections. Deinterlacing such games in the normal field combination method generally results in combing artifacts where there shouldn’t be any, whereas linedoubling 288p games that were converted to 576i surprisingly retains the original visual intention. But for the vast majority of games that were rendered at 576i to begin with, you’re better off letting your TV or some other device do the deinterlacing. Even a cheap scaler will produce a more accurate deinterlace of such content than the OSSC or RetroTINK.