No, setting colour won’t stop them working. The PS2, from any region, is capable of outputting every other region. Sony just disabled the option to do so, the chip gets around that.
As the PS2 will default to the region of the software and not the hardware, JP games will be fine as they also use NTSC.
You might also want to try disabling Macrovision. While not strictly for games, it can sometimes help.
As for the firmware, it doesn’t sound like you’re using 1.93.
The Modbo 5’s came with a modified version of the 1.93 firmware with some hacks and changes and frankly, they fucked it up. It has all kinds of compatibility issues with a lot of games.
If the firmware has never been changed from the one it came with, that could be a part of your problem.
As an aside. Have you considered using Free McBoot. Sure it involves some more purchases. Ideally a hard drive and a network adapter and of course the memory card with Free McBoot on it.
I personally prefer that option, it’s nice to have all the games stored on an internal hard drive. No swapping discs, or wearing out the laser.
Not to mention the PS2 is far more compatible and versatile, in that it can run homebrew easily. If you’re into that kind of thing.
You can do it with just the mem card and a usb Drive, but it’s damn slow doing it that way.
You can get third-party hard drive adapters really cheaply, or, the better option. Pick up an official Sony Network Adapter as cheaply as you can and a SATA converter.