Brindisi to Amalfi

Driving is not difficult, and you would drop the car at Salerno, then take a bus or ferry to Amalfi.
Have you checked bus options?

I have not checked bus options. I might be able to get a driver for that short distance? I do like the idea of a boat. Thanks

I am actually touring around Italy for 47 days and traveling light. The only long train ride, it appears, is when I travel from Florence to Barletta

I guess it just depends on how much time you have at your disposal and your level of aversion to driving.
There is no boat connection between Brindisi and Amalfi.
Check skyscanner for flights.

An overview of options here--- https://www.rome2rio.com/map/Brindisi/Amalfi-Italy

Train routes across southern Italy are rarely fast or direct. But you can make the train trip from Brindisi to either Napoli Centrale or Salerno train stations with just one connection, most options taking 5-6 hours. The 7:54 departure with connection at Taranto is the closest to taking the 7 hours you anticipated to Naples, but the same train stops at Salerno 40 minutes earlier, so I'd use that stop.

If driving, I wouldn't particularly drive to save time, but would drive if you wanted to visit other stops along the way. Are you visiting Matera, for instance?

I am planning on making a day trip to Matera out of either Barletta or Brindisi. Thanks for the idea on stopping in Salerno.

From Bari to Matera is about 45 minutes by car, not sure about transit time from Barletta. Stopping for a night in Matera would be a great idea--the sunsets can be quite lovely, day trippers will have departed, plus it would break up your journey.