How to prove/deal with plagiarism that is hidden behind bad synonyms? I have had more than one undergraduate student who I have very strongly suspected of routine plagiarism that I cannot prove. There is a certain style of writing that is just inexplicable except as an effort to avoid plagiarism detection.

I will give an example from a case I was actually able to prove. The student wrote:


  Free enterprise prejudice is changing in the current period as another U.S. racial conviction framework at a moment that African Americans are a vigorously urbanized, broadly scattered, and occupationally heterogeneous group; when state arrangement is formally race nonpartisan and focused on anti discrimination endeavors; and when most white Americans lean toward a more volitional and social, rather than innate and organic, translation of blacks' burdened status.


This was clearly an attempt to plagiarize from one of the readings in the course:


  Laissez Faire Racism is crystallizing in the current period as a new American racial belief system at a point when African Americans are a heavily urbanized, nationally dispersed and occupationally heterogeneous population; when state policy is formally race-neutral and committed to anti-discrimination; and when most white Americans prefer a more volitional and cultural, as opposed to inherent and biological, interpretation of blacks' disadvantaged status.


This kind of plagiarism is totally missed by SafeAssign, the detection tool that I have access to. When I am able to prove cases like this, it's only with much effort. Of course, I can just give students F for writing incoherently, but I would like to have these students removed from the course. I can only do it if I can prove the plagiarism. 

Can anyone recommend any strategies for dealing with this? 

EDIT: I of course do try to explain to the student that this is not an appropriate way to paraphrase. They typically say that they understand... and then they do the exact same thing on the next assignment.
To me it is not obvious that your example is a "clearly an attempt to plagiarize". It looks to me like an attempt to paraphrase. Most students that I see who cheat are too lazy to be bothered to change any words. If the original source was referenced, I would not pursue the academic misconduct route. Instead I would give a poor mark for writing incoherently and not showing any depth of understanding. I might also focus an activity on proper paraphrasing and how paraphrasing does not generally demonstrate depth of understanding.

If the source of the paraphrased/copied material was not referenced, then the situation is more difficult. I would probably first consider if the simple lack of a reference is academic misconduct independent of the copied material. If it is not, then you need to decide if the two actions are academic misconduct. Again, I would probably give the benefit of the doubt and conduct a referencing activity. After the activity, I would let the hammer fall.