In addition to what you found broken on the shifter, there is a bolt for the trans linkage that can be adjusted to match the shifter position. After I installed the body lift, I had to adjust the linkage bolt to correctly postion the shifter, otherwise I couldn't remove the key without pushing the shifter forward (like you). By not fixing the problem for a few weeks, I developed a leak on the shift shaft seal from putting unwanted stress on the seal when pushing the shifter forward.

I ended up adjusting the bolt correctly by making sure the transmission was in park, then adjusting the bolt to match the shifter in the fully locked park position.

You might as well replace the sleeve first, but keep this in mind if that doesn't solve the problem.

Here's a pic of the linkage.