Ollie your going in peak season so it will be busy, fully of Europeans. You say the Americans are not on holiday but its not them you need to worry about its us lot lol.
It all depends what you want to see and do. If there are 2 showings of Fantasmic then go to the later showing its less busy and you can get there an hour before.
When you go to the Magic Kingdom get there an hour before opening as it will take you 30 mins to get from the car to the park and then head straight under the castle and get the small rides done. By doing that you will save time later on. You will not get round the Magic Kingdom in a day and get everything done, its impossible during peak times.
Hollywood Studios, head straight for Toy Story as again you will get stuck in 2 hour queues if you leave it and fast passes go within the hour, this even happened when the park was not busy. Also get a fast pass for RnR as the queue for that even off peak is large, ToT has huge through put I have never seen a queue longer that 45 mins.
Epcot is hard to judge but head straight for Sorin and either ride it or get a fast pass, queues are huge for this ride. You will probably need a fast pass for Test Track as well, queues build up fast and its rather slow moving.
Good luck with Harry Potter World, and again IoA/Universal car park is about 30 mins away from the park.