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.

Moss page states:

it shouldn't matter whether the suspect code was first discovered by Moss or by a human; the case that there was plagiarism should stand on its own.

If you want an automated method of discovering every cheat, wait until the Singularity. Lazy students will always find the way to get past the alarms with minimal work. You can spend months making your software understand synonyms, and they will just spend ten more minutes reordering the sentences.

I think you have sufficient evidence to start the procedures, it doesn't matter it was you or the software who detected it. Anyway, I hope there are not too many individuals like this, in which case you should do something public education at a larger scale.

Also, consider having a talk with the student. Maybe he doesn't think that it is plagiarism.

Well, in this case it sounds like you caught the plagiarism without needing to use the software. How? Because the student plagiarized from one of the course readings, and as it happens you are very familiar with the course readings.

It seems to me that this "human plagiarism catching" can be generalized: you don't have to be able to have software to trawl the internet for copying if you yourself know -- or even have a sufficiently good idea -- which material is likely to be plagiarized. In my experience the average student is remarkably bad at getting academic information from the internet: they don't know enough to rapidly and accurately sift through the deluge, so they hold tight to whatever was high on the first google search screen and succeed or fail accordingly. If you are concerned about plagiarism, I think it would be time well spent to search the internet before making the assignment and bookmark the most plausible sources to be plagiarized. This won't catch everyone, but then again nothing will. If you feel strongly enough, you might even design some initial assignments as "plagiarism bait". As long as your goal is to teach your students right and wrong rather than a priori to get them in trouble, I think this is an entirely justifiable thing to do. Also showing someone that they have already gotten caught and gotten in some trouble can be a great motivator for keeping their nose clean in the future (or, sure, digging much deeper in their dishonesty, but again one has to play the percentages here).

Good luck. I don't work in a field in which plagiarism in papers is common -- I am a mathematician -- and the idea that university students regularly commit such dishonorable acts disgusts me. Anyone who wants to take a harder line (and of course who informs and educates the students in advance) has my full support.