Take off the front tray cover (either by unscrewing or breaking off, I recommend unscrewing) then turn on ps2 without a game inside, and go to browser, then put in a real ps1 game like you'd normally would. Once it's loaded, use your swap tool to take it out, and put in the burned cd, then close the tray and use the swap tool to lock it back in place. Highlight the cd and press x, and enjoy ^_^
This is the easiest way to play ps1 backups that I can think of, besides modding your ps2 (whether hard or soft)