The first two weeks in September will be a sight less crowded than August. My guess is that you'll find more space available as you cover the distance. The longer you're there, the quieter it should be, but more people will hit the hills at weekends.
Whether you choose to stay in refuges or camp, you'll need a sleeping bag. If you want to take a chance and hope there's room in the refuges every night, then you won't need a therm-a-rest, since they provide foam mattresses on the bunks. If you're going to camp at any point, a therm-a-rest makes all the difference, since the ground is nearly always hard and stony.
If your flight into Bastia is delayed, it doesn't necessarily mean you miss your bus. There might be time to grab a taxi from the airport to get you to the roadside at Casamozza just in time for the bus!
When you get to Ste. Lucie, the best thing is to phone the Gite d'Etape La Tonnelle at Conca, tel 04 95 71 46 55, and see if they can give you a lift. Naturally, only do this if you intend staying the night at the gite. The guy running the place speaks English, if your French isn't up to phone call standard.
Pack enough food for the whole of the first day, then start early while it's still cool, and take your time. It's not a hard stretch, but when I last did it, I found a local fisherman severely dehydrated under the shade of a bush, and felt obliged to offer him water. He drank nearly all of my 2 litre allowance, and if it wasn't for the tiny trickle of a spring near Capeddu, my trip might have been totally scuppered!
£79 is a great price, and you're lucky you can fly from Gatwick. That's an awkward place for me to reach, and flights from my nearest airport are much more costly.
I have my own copy of the updated guide now, and despite everything I say about keeping the pack weight down, the extra info in the new guide means it's 100g heavier than the previous edition. Sorry!