Although I haven't used it, the Porta Marina luggage check gets high ratings from everyone at this newsboard. Pompeii may not have its own tours - are you referring simply to Cruise Ship crowds? This is such a large site that crowds aren't a big problem. The only lines are at the bathrooms, the snack bar, and the brothel. You can't avoid those lines. I'd guess that ship tours get to skip the Brothel line anyway. We found a few sprinkles to be relief from late May heat. But of course you don't want to visit in the rain.
My own priority is for avoiding mid-day and afternoon heat and sun. The site is very exposed. I would take an umbrella for sun protection if anyone is sensitive. Pompeii is very worth the trouble to visit, regardless of when you go. If you are exhausted from the flight (what country are you coming from?) it might be less fun. Where are you sleeping?
I only mention this as an option: The Villa of the Mysteries, besides its art-historical importance (IF IT IS OPEN!) is off the beaten track and might have thinner crowds. But it is a long walk. It's almost faster to use the street entrance near it, but you CANNOT re-enter Pompeii with the same-day ticket!