Hi, anti-Path of the Gods guy here. Three nights is just two full days, and I would not use one of these on PotG. It makes for a long day, and may wear you out. Also, not sure what that tour company is doing… it starts in Sorrento? Or is that just where they pick up? The most traveled and scenic part of the trail runs between Bomerano and Positano, so you may be expending effort to go all the way to Sorrento just land back where you started. A guide for PotG would be kind of a waste anyway, it’s well marked and extremely well traveled.
Capri is totally worth doing as a day trip if you can get there early enough. Coming from Positano there may not be a very early ferry (they launch from Salerno.) Avoid the crowds by skipping past Capri Town and get up to Anacapri. Take the chairlift up to Monte Solaro. The crowds really don’t make their way up to Anacapri until the afternoon. In the morning, it’s positively tranquil. Capri Town is a tourist trap.
I would suggest a day exploring Ravello and Amalfi before PatG. The views from Ravello and Villa Cimbrone are much the same as you get on the hike (and you can have a glass of wine while you admire them!) Ferry to Amalfi and then bus (or splurge taxi) up to Ravello. I absolutely love Ravello, and Ristorante Salvatore was one of the best meals I had in all of Italy.