Ok, if you are not able to swap the cds by checking the disc speed change, then just use this time-trick.
Use a backup copy with our patch on it.

Turn-off your PS2
Insert the original PS2 Utility Disk cd
Place the White Disk (Locker)
Now, check your watch (seconds)
Press the Reset button to Turn-on the PS2
Wait 10 seconds

Ok, not it's the time to swap, you have 5-10 seconds to swap disks
Remove the White Disk (Locker), Remove the original CD
Insert the backup copy and place the White Disk (locker)

Ok, now you have the backup copy working.

Remember: 10 seconds after you pressed the Reset Button and then 5-10 seconds to change the disk.