Naples is a substantial, very historic city. I like it, but you can't see much of it during the time span you have sketched out. You state clearly that your objectives are limited, and since you must change train lines (at the same station) in Naples, it's not a big deal to "glance" at Naples. I think you'll have no time wasted checking luggage?
There will be no line for Pompeii tickets in January, but you should be ready (back in Rome, I mean) with warm clothes and rain gear, if the final weather forecast indicates it. The plan for Circumvesuviana tickets is simply to buy two tickets for each of you when you are at the human attended window in Naples, on your way TO Pompeii. I imagine the reported long line was for multiple non-Italian language speakers learning how to use a single (?) vending MACHINE at the Pompeii Circumvesuviana station. If you already have a ticket, you simply have to Validate it before boarding in the machine mounted on the wall. Do not board without validating.
I personally WOULD buy advance Frecciarossa tickets for Rome-Naples-Rome because the cost savings are huge. You are planning a complex trip and it is not a burden to make firm assumptions about your allocation of time for the day. (I'm saying that even if the weather is good and you LOOOOOOve Pompeii, you cannot allocate more than four hours to your visit. But they are Non-changeable and Non-refundable train tickets.
You won't even have to wait on the sidewalk for 70 minutes for a pizza seat like we did in summer high season. But if you live near a city with an "authorized Neapolitan pizza oven" (hemispherical, tiled, maker's name, etc.) restaurant, you don't really need to spend time just to have "pizza in Naples." Of course the Italian ingredients are better, but it wasn't that different from the multiple authentic oven pies I've had in Manhattan and at Arthur Avenue, Bronx.
I'm surprised no one has told you must go to the Archaeology Museum in Naples. But on your schedule, unless the is an Art History major in the group, you don't have to go there.