How to prove/deal with plagiarism that is hidden behind bad synonyms?
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.