Car Service from Naples to the Amalfi Coast

Actually given the distance that sounds pretty good. Remember for something like that you probably are paying for both ways since it is unlikely that the car service could find a return trip. You could take the train to Sorrento and a taxi from there. That would be cheaper but a little more inconvenient.

Your hope is unreasonable. That is market rate. This is a long, slow drive, with a likely empty-return. I always ask my hotel to recommend their local land-partner, thinking that they will have a high motivation to provide good service. When staying in Sorrento, the cars all turned out to be new-ish Mercedes four-door sedans with air conditioning and leather seats.

Make your departure plans now as well. This is not a "remote" location but it is "isolated." Many people are startled at how long their next move will take after the AC.

I am not one who hesitates to spend money, but a train to Salerno and ferry to Amalfi actually sounds more pleasant, unless ferries are not running when you will be there.

Another alternative is taking the train to Salerno and then the ferry to Amalfi. This alternative may be faster and cheaper.

...a train to Salerno and ferry to Amalfi actually sounds more
pleasant, unless ferries are not running when you will be there.

This is key as ferries do not run to all locations around the coast during the off season. When will you be traveling?

We will arrive in Naples on November 11th. We will need car service on the 12th. I get the idea the ferries stop running at the end of October.

This old thread includes the info on our car service:

https://community.ricksteves.com/travel-forum/italy/amalfi-coast-day-trip

What about train to Salerno from Naples (very inexpensive) and car service from there?

That aside, this car service has been highly rated with RS posters whom have used them, including Rick himself. I've no idea what the cost is from either Naples to Amalfi or Salerno to Amalfi but you could contact them for a quote:

http://www.monettitaxi17.it/English.htm

Just some of the threads where they're reco'd:
https://community.ricksteves.com/travel-forum/italy/monetti-taxi
https://community.ricksteves.com/travel-forum/italy/contacting-monetti-taxi
https://community.ricksteves.com/travel-forum/italy/amalfi-coast-driver-monetti-or-del-pizzo
https://community.ricksteves.com/travel-forum/trip-reports/wonderful-guide-on-the-amalfi-coast
https://community.ricksteves.com/travel-forum/italy/naples-airport-to-positano-cf0321e6-0085-484e-9a1b-0bf2274b3fce

We stayed in Naples this summer for 5 days and one of the days we used Monetti Taxi service to see the Amalfi coast. I highly recommend their taxi service. Although they will come to Naples to pick you up and drop off we didn't do that. We took the train to Sorrento from Naples (and then back from Sorrento to Naples at the end of our tour with them). They live in Sorrento so meeting up with them at the train station there is a lot cheaper than having them transport you to and from Naples. We did book with them well in advance. It was a wonderful way to see the Amalfi coast. Have a great trip.

We used topexcursionsorrento.com for 3 different days during our Amalfi Coast vacation.

They were great---not inexpensive but well worth the money. The owner is Giovanni and he will totally enhance your appreciation of this beautiful area.

I have nothing against Monetti and have never used them. But I could see from their posted rates in a vehicle of theirs I saw near the Circumvesuviana station that their flat rates were not the lowest, maybe 10% higher. Perhaps the service is worth it. I did like the visible-posting of the flat rates, because our unmetered taxi (the "next" guy in line .. ) charged us 15 Euros from the Circumvesuviana Sorrento Station to the Ambasciatori Hotel, about 800 meters!

The least expensive and fastest way is train from Napoli Centrale to Salerno. Time 39-47 minutes.
€5,23. Use the regional express or intercity trains. Then a taxi Salerno-Amalfi. 30 minutes, about €55. Even if you add a taxi to Napoli Centrale you'll be under €80.