I did it on a fat model using the Metal Gear Solid 3 and memory card trick. I did this about 6 months ago and streamed the games over a network instead of disc and USB 1.0 read speeds are to slow, its like playing the commodore 64 with a tape drive. It's a lot easier to get a copy of freeMcboot on a memory card as you already need a specific game.

the game tries to load the level, and you boot into Free McBoot. you run the game with the original and after you pass the check, you swap the disc. you rip AUF onto your HDD, replace a file with the loader. You basically get to a certain part of the game, then save. I've wrote guides on this in the past, but I don't have any links or resources as I legit don't remember where to get the files you need. Agent under fire is the game to use but not the greatest hits version. For the fat model you'll have to open it up, but the process is the same. If you own a slim, you can just use something to press the button down to make the ps2 think the door is down then swap the disc. If you have a PS2 Slim model and want to softmod, look into a custom lid that has an opening that doesn't trigger the DVD drive to stop running when you open it and look into a memory card with Free Mc Boot on it and whatever disc swapping software of your choice. Well, if you're trying to play pirated games, I can't help you with that, but softmodding alone doesn't make the PS2 capable of playing burned games any more than a regular console.

Ps2 softmod