Regarding Summary Judgment and Time Frames

With a few specific exceptions, virtually every time limit can be relaxed by the court. So the answer to your question is it depends upon what the Judge in your case says. You can certainly raise this issue, but you should also meet the substantive arguments made, just to be sure you don't lose because you didn't do that. Better still, go talk to a lawyer.

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Call the judge's law clerk, advise him or her that the other side filed a late SJ motion (which seems to be the case), and ask how the Court wants to handle the situation. If the case actually goes to trial on July 27, the summary judgment motion will probably never see the light of day. But if the trial gets delayed (which is pretty likely), you will have to defend against the motion.

Good luck!

This answer is given for educational purposes only. I don't know nearly enough about your case to make any advice I give you reliable. Unless and until I agree in writing to become your lawyer, nothing I say should be interpreted as legal advice.

Note that the rule goes on to state that "...unless the court otherwise orders for good cause shown, and if the decision is not communicated to the parties at least 10 days prior to the scheduled trial date, an application for adjournment shall be liberally granted..." The Court has discretion to control the calendar as noted in one of the other answers above so it most likely depends on what the judge orders.

3) Since the judge would rather they did not move to delay the trial first, then submit it 30 days before the new date, the judge can be lenient and accept the motion.
After all, if the motion is good enough to win, the trial is a waste of time and the motion saves both sides and the court time and money. If it is good enough to win, it basically means "Assume everything the other side says is true. They still can't win". And if that's the case, why have a trial?

This should not be considered legal advice and is intended for educational purposes only. It does not constitute a contract for legal services between any parties. Answers are given to questions for which there may be additional facts not mentioned which might change the legal issues or consequences.