I just got done doing mine... Using the GM grease kit that comes with the plug to push the grease down in the shaft..
I used instructions from a different site that had pics more geared for a 2003... The instructions above really aren't that close to what you will see. They look like they are geared for the pre-2000 Bonneville.
I did NOT clean the shaft before putting the new GM grease in. It did work much better when I got done, but wish I could have flushed the old stuff out, dry it somehow or wait, then put the new grease in. I really think the grease GM is using sucks..
I picked up a F150 with the typical truck- driveline slip yoke "clunk" which is actually a similar problem as what you feel in the steering right now.. Everyone is using Mercury 2-4-c Marine grease with Teflon which I bet is a better grease than GM.. I will be pulling my shaft once again and going this route as it has already popped once or twice..
Hope this helps..
2003 Ivory -hard loaded but stock- Bonneville SSEi ::Luxury with Attitude::
88 Bright Red Pontiac GTA L98 - "Gone but not forgotten"