La Spezia and Naples- Disembarking mega ships for port tours

It depends. Often cruise lines give priority to passengers going on their tours and then allow others to depart.

Check with the cruise lines.

A 0700 arrival doesn't mean the gangway will be open then. It could take half an hour to complete formalities and prepare for disembarkation. But if you can get off the ship promptly and grab a taxi to the train station, you could be at the Pisa Centrale station shortly after 0900. Where do you meet your tour?

As for Naples- the ship should be docked, not moored, so you can leave the ship as soon as the gangway opens. If you are being picked up at the cruise terminal, you should be fine

I checked with Princess and they said there would be a delay for port clearance. However, I don't know if they give preferential disembarkation to their own excursion passengers. Do any Princess cruisers know? Also, would a mega ship like the Sun Princess have 2 or more exit gangways?

Luckily I found an operator that has a Spezia cruise pick-up for their Pisa tour so I assume we can make that by 930am. However, I still worry about having only 1 hour in Naples.

I've posted elsewhere that it's a bad idea to go on excursions that the cruise line hasn't organized. It's a good way to get left behind at the dock with an expensive trip to the next port of call at your own expense. It's happened to several people I know.

If you don't like your cruise line's excursions, pick another cruise line.

Have you checked Cruise Critic for this information? I think you’ll more fellow Princess cruisers that could give you insight.

Sun Princess can use 2 gangways for passengers, depending on the pier they are at. Princess typically does not give priority to their own excursions at non tendered ports, but DO escort each excursion group to the gangway at the appropriate time ( which may or may not be first thing). Just make your way to the line leading to the gangway as soon as the ship docks, and wait.

As for the comment about risks of independant excursions: millions of experienced cruisers would disagree. But a degree of due diligence and judgement is required. An excursion requiring hours of travel to and from the site might be more prudently booked through the ship. But the risk of missing the ship if the excursion is more local, and especially if the return time is stated to be well before the All Aboard time, is slight. Keep in mind that independent tour providers depend on reviews to stay in business. If they miss a sailaway, they don't stay in business. We rarely book a ship excursion, and in 20 years have never missed a sailaway.

An excursion requiring hours of travel to and from the site might be more prudently booked through the ship.

The excursions under discussion here fall within this category IMO. But everyone should take whatever risks they feel comfortable with. I'll also note that cruising on a "megaship" is not in my experience, nor will it be.

Port arrival times are always an aim, not a guarantee. Many things can delay a ship at sea such as bad weather, breakdown, medivac, responding to an SOS etc. Furthermore when a ship reaches any port it has to embark a pilot-(s)he can be delayed for all manner of reasons. So you might arrive outside port on time or even early but then wait and wait for a pilot. My record for that was almost 8 hours waiting at London Tilbury, due to heavy weather making pilot transfer unsafe.
If booking an independent tour no experienced UK cruiser would travel without missed port insurance to cover for such eventualities.
When a ship does dock there is a lot of paperwork to do before people can disembark. Unless it is a rare port with an 'airbridge' the gangways and security points have to be set up, normally concurrently with the ship's clearance. But that all takes time.
Although you should be off (if docked on time) before the ship's excursions (normally such people are given time for breakfast first) I think 8am in Naples is very significantly optimistic. I have never had a pre-booked independent tour in any port, but rarely take a ships excursion either. I explore on my own or sometimes book tours on the quay when I arrive.
If running tight for time as you are I always have an earlybird continental light breakfast rather than waiting for the full cooked breakfast.

I agree with Patty. Go to the Princess forum on Cruise Critic. They will be able to give you first hand knowledge.

Will the ship be at a dock or might it be anchored in the harbor and necessitate taking a water taxi to shore?

The latter is likely a slower process. The cruise line should be able to tell you where the boat parks.