While taking it and getting it over seems to be the consensus...
I'm in the same boat as you. Getting less than a 170 would not be desirable and taking the June test is not imperative on me.
Have you checked all other materials? There's a difference between getting a question right and knowing why you got the question right. I just finished a Princeton Review course tonight. I haven't worked the Nova "master the lsat" nor have a fully worked the Powerscore logic games bible. Those are two sources I'll be working on in the meantime.
As far as the preptests are concerned, I would rework each one of them. They no longer hold any value as indicators (since they're old material) but looking over the entire pile will allow you to see patterns and make connections not previously possible.
If you give yourself more time, you will at least know conclusively that you've done everything you could. If you take it in June and you don't feel as prepared as you should, then you'll kick yourself in July for being hasty. It's not the SAT, you should only take it once.
Sit for the June test, sleep on it, the next morning you can decide to keep it or cancel it. Do that much at least.