I don't think you need any patches to anything. You should already have what you need.
Whether it works depends on what version of the code handler is included. If you apply the code, and then go to Memory Viewer, 800028B8, and you see "00D0C0DE", then it's probably using the right code handler. Look for the F6 code. It should now be F6000301, and that means it managed to find the Z values (which means it could then hook). F6000101 means it failed to find Z values, so the hook is not executed.
EDIT:
Hit post too early. I don't know what videos you found, but just buy replacement sticks from amazon or ebay. Then use this video
http://www.youtube.com/watch?v=kHYjUdZyZoU or you can use this guide but everything beyond step 4 isn't needed to replace the stick.
http://codebook.potchgult.com/stickrepair/stickfix.htm