If you still have timing issues, I would advise you NOT to take it in June.
Unless you have specific reasons for needing to take it now, it is difficult master timing in just a few weeks... why not the Oct LSAT?
Timing is usually the last thing to perfect (after accuracy). So you should dissect the questions you run out of time for - is it literally just timing, or is it more accuracy (i.e. if you had more familiarity w/a certain question type, you wouldn't need as much time with the question)? Because to practice timing, you just need to do more timed PT's. But if it is more an accuracy/familiarity thing, untimed drilling and reviewing would be beneficial for you.
However both of these things take awhile to perfect. I think you can definitely score in the range you want but if you're still having trouble with finishing under the clock for 2 out of the 4 sections, it seems like you are definitely sacrificing some points by taking it in June, no?