While I like both Kona and LTT, we always prefer the food choices at Epcot. How about Chefs de France or even Le Cellier. Might be a tiny bit easier than usual to get an ADR for lunch at Le Cellier especially since you said you want a late lunch.
LTT and Kona are both great for lunch. But Kona closes at 2:30. Not sure how late you're planning to dine.
We also love Chefs and Grand Floridian Cafe (closes at 2pm). We haven't had lunch at Tutto Italia but dinner there is great....I bet lunch is too. You will probably have better luck with a very late lunch at the parks. Most TS restaurants at hotels close between lunch and dinner. Beaches and Cream is the only exception I can recall.
If you have a car, the Sand Trap at Bonnet Creek Golf Club is a nice peaceful spot for a good lunch and they do serve all afternoon.
If you get an ADR for Crystal Palace about 2:40 or so, you will have access to the dinner food at 3PM. And they usually have prime rib on the dinner menu. It's not crowded at all at that time, plus you pay for the lunch rate, not the dinner rate. And you get the best of both - as long as you get the lunch items you want before they start removing them for the dinner food.
We always eat at LTT for our lunch on the last day we are there. It's the last thing we do. The pot roast is excellent.