This game uses a disk swapping feature. You remove the game disk, put in another disk and it creates a monster based off something on that disk and then you replace the original monster rancher disk.
So the question comes to, would I be able to use a backup of Monster Rancher 4 and use that feature or not?
Ah the fliptop? Been wanting to get one of those just for fun :)
Have you tried swapping discs without ejecting the tray? I remember Monster Rancher 2 for the PSX wasn't able to do that, but you never know lol.
About the flip top, when you flip open to swap discs, is there a magnet in the center or is it a white plastic cirlce in the middle of the flip top? I ask because I have an idea but I don't want your backups and/or PS2 to get messed up.
My idea is, when you want to get a monster from another disc, to eject the tray and replace with another disc as usual, then when it comes time to eject and replace with MR4, replace with Swap Magic and let the PS2 read it for a few seconds, then flip the top and replace with your backup copy of MR4. If after a few tries and it doesn't work, try using an original PS2 game.