I imagine that that elderly sheet is still in effect. I had no trouble opening the link that gerri provided. I wish I could remember if there was a dispatcher at the airport, but I don't.
Note that Fixed Rates include all extras. That's on the sheet. It is quite common, however, for Naples taxi drivers (perhaps because the rate sheet has not been updated, as you noted) to try to charge for luggage IN ADDITION to collecting the flat rate. If you know what the flat rate is, you can detect if he's collecting a tiny amount, or really ripping you off. If you have printed out the sheet and brought it with you, you could wave it in his face.
Of course, it might be wise to ask about the rate BEFORE you get into the cab. But he might still (because Neapolitans are so ... entreprenurial, like Tech Bro's ... ) try to add luggage fees when you get out. But this is no different from taxi worries in New York City and anywhere else. You said you've traveled a lot! So you are over-reacting a bit, but you don't seem to have all the facts (like the Rate Sheet) at your fingertips.
I don't see that risk of a 2 or 4 Euro phony luggage charge cancels out the benefit of refusing a 60 Euro private car transfer. And that's if you decided to roll with it, and pay the 2 to 4 Euros.
If you really think you'll be that exhausted, you might pre-prepare a sheet of paper with the address of the hotel on it, along with quotes (In Italian, naturally) from the Fixed Rate Sheet. If you use the exact words from the sheet, he'll figure out that you have a copy of the sheet. Naturally, you would include the words "comprende ogni extra."