So, I got bored and decided to find out if this was actually feasible. I've managed to do it, but it achieves nothing of interest. If I could fix the filtering I might be onto something, but that will take 100x more work. It's >30 degrees C here and the cooler is broken, so I'd rather drink beer and play games.
Whether or not the display is interlaced is controlled by the CRTC (CRT controller). It is initialized by the running program. It's possible to patch the program so it will make the CRTC to run in deinterlaced mode. This is what I've done.
I was hoping the deinterlaced display would at least fix the weirdness you get when scrolling horizontally (in tate mode - moving along the screen's short axis) - scrolling left and scrolling right feel very different. Unfortunately, it didn't work. The deinterlacing seems to cause it to alternate between the even and odd lines of the image, so the image distorts somewhat as it scrolls. It's only really noticable in the background in either video mode. It fixed that particular problem, but introduced another equally bad one.
Anyway, the patch:
01 00 24 32 ff 00 45 32
00 00 04 20 ff 00 45 32
01 00 24 32 04 00 06 a6
00 00 04 20 04 00 06 a6
I leave the actual method of patching to you, as I can't think of any that don't involve copyright infringement. It might be possible with some sort of cheat device, but I can't find anything on how to create the codes. It's not the sort you're likely to go to hell for, but it's still illegal. Again, in the end this doesn't do anything useful unless you have a fetish for scanlines. It doesn't make the game any more fun to play.
(The code is MIPS machine code, if you're interested. If you want to see how it actually works read Dreamtime's PS2 programming tutorials and mess around with the code. Knowing MIPS assembly will help immensely.)
The same strings work on Ibara. The results are somewhat better. The lack of interlacing seems to make the filtering more apparent.