UPDATE: Lee recommends using a new clutch when changing to the soft twist because a clutch that has been used/formed to the regular twist does not work well with the soft twist.
I had the problem and replaced the clutch. That fixed the issue...at least for now. I was having the same exact problem. The inside of the clutch had a bit of buggered up corner and I assumed that was what it was...now I see it probably wasn't the issue. Here's the easy way to see if the issue is too much play...simply put your finger down on the top of the rod and apply pressure while operating the ram. As soon as I did that, the problem went away. I will keep the old clutch knowing that it probably wasn't too badly damaged...I bet the tape trick would have been just fine for my issue.
This problem goes away for me by lifting up the twist rod, turning it 90 degrees and lowering it in again. The driving clutch is a cross and it seems one direction is tighter.