@JenSchroeck -
I just re-read my post. I think the work around will work - more or less. The only problem is the extra assignment has to be assigned to only those who scored lower than 60%(not a problem), but the module will show up for all students. So students who scored >60% will see an empty module and may be confused. So, there would have to be a document in the module explaining what its existence is for.
On the plus side, if there are multiple assignments where the >60% criteria will be applied, all of the extra attempt quizzes can be put in that module with each one assigned only to those students that require it. You could name the module in some way that also implies what assignments would be there.
obviously not a great solution, but a plausible work around - provided the information can be explained to the students..