[neodude237]

I know this is going to sound really, really odd, but this *may* work for you. (Try it if you want, it is a bit risky if you do it wrong, and can scratch your discs up bad, but you might want to try it once to see if it at least works.)
1: Boot up your PS2 with no disc inside and take it to the browser.
2: Put a normal, North American disc in (while you still at the browser)
3. It should show up as a picture of a disc in the browser now
4: Now, flip open the flip top lid
5: Take out the North American PS2 game, while it is spinning (do this as carefully as possible)
6: Place the Para Para Paradise game in while the center part is still spinning
7: select the disc icon in the browser and start it


I know that is an awkward method, but it may just work as an alternative method for you. Again, try this at your own risk. (The reason I am bringing up this method is that it works for me to boot PS1 imports, so it may work as an alternative PS2 import boot method as opposed to swap magic)