How many days to stay on Amalfi Coast, and where to stay last minute?

Q: is it worth the trip?
A: Yes, IMO

Q: Can we find accommodation on short notice?
A: Yes, but weekends get busy in June. You should stay a minimum of 4 nights to make it worthwhile.

Q: Can you get to any less crowded beaches by bus?
A: Yes. The buses travel back and forth from Sorrento to Amalfi, and another bus travels from Amalfi to Salerno. They make stops along the way at all bus stops upon request. There are scores of beaches (mostly small pebbly coves since the area is just cliffs) along the entire coast, so you can reach any you wish by bus. They might require some walking, often down rocky cliffs to reach since the road is often well above sea level.

Q: Maybe it is just too far for 5 or 6 days?
A: It's up to you. How do you intend to travel from Amalfi coast to Slovenia? It's a very long trip and there are no direct non stop flights from Naples.

You probably don't need Italian rail passes. Your train travel is not extensive enough to make it worthwhile. A cheaper alternative is to pre-purchase online Economy or SuperEconomy tickets (up to 120 days in advance). Be aware those discounted fares are non refundable or changeable, therefore if you miss the specific train you book, you lose your money.

You might check booking.com for last-minute availability (you can check listings or sign up for last-minute alerts, but checking the listings is best). If Positano and Ravello are full, try some lesser-visited towns (Praiano, for example) along the coast.

Are Florence-Naples and Naples-Venice your only two train travel days? 2nd-class fares for fast trains on these two routes add up to $250 full price per adult or as low as $100 if you're ready to lock in advance rates for particular trains about three months out. If you don't book hotels ahead, then I would not book trains ahead.

A 3-day Eurail Italy rail pass costs $155 per adult in 2nd class, plus $30 for two seat reservation fees (which you can make on the day of travel, if your class of service is not full, or one day ahead, etc). Your trips are longer than what many travelers plan, so the pass value works out better. Of course, you maximize the value if you use the third travel day.

Either option has good deals for kids. See also https://www.ricksteves.com/travel-tips/transportation/trains/italy-rail-passes.

Train is not the most direct way to reach Slovenia. If you just want to cross the border along the coast, you can take a bus from Trieste. DRD and GoOpti operate other shuttles that you can book to depart from Venice to Ljubljana, etc.

We just came back from a two week trip that included 8 nights in Sorrento and the Amalfi Coast. Even in April there was a huge traffic jam in Positano that threw the buses from Sorrento off schedule. The buses were so packed, there were no views except for those lucky enough to get a seat on the window side. Don't count on being first in line to board the bus. There is no such thing. Everyone piles on en masse. It is not considered rude, it is just the way they do it. Since you are coming from so far away, I recommend you take the fast train through Rome to Salerno. This will be much quicker than the Naples, Sorrento route, and Salerno is not crowded with tourists. Then take the SITA bus to the town of Amalfi and sleep there. There are several quiet small towns near Amalfi that you can visit. Maiori is a very small, quiet town with a couple hotels and restaurants and quite close to Amalfi, Ravello, and not far from Positano. So an even quieter option might be to sleep in Maiori if there is easy access to the beach.

2nd-class fares for fast trains on these two routes add up to $250 full price per adult or as low as $100 if you're ready to lock in advance rates for particular trains about three months out.

That seems wacky. I just looked for Sunday, day after tomorrow. Full price flex fare one way per adult standard class walk up flex fare (the highest second class fare) on Italo Treno (Trenitalia would be similar) Napoli Centrale to Venezia Santa Lucia is €89 per adult. That's $101 US. The Napoli Firenze will be much less. Where oh where did $250 come from?

2nd-class fares for fast trains on these two routes add up to $250 full price per adult or as low as $100 if you're ready to lock in >advance rates for particular trains about three months out.

Now that I've had a night's sleep I've had a chance to look at the fare from Florence to Naples as a walk-up. Looking at tomorrow it is €64.90.

So €64.90 plus €89 = €153.90 which is around $175. That is a far chalk off the $250 used to justify a railpass.

So that is $10 less than buying a pass and then having the hassle of getting pass holder reservations.

You might find it interesting that both last night and now I can find several trains which still have discounted seats, as low as €54 for the trip to Venice.