There are zero airlines offering flights to Shanghai. The most direct route isn’t necessarily the cheapest – being flexible is key to finding the lowest airfare rates. For example, try searching by month to see the best time of the week to fly.
Shanghai Pu Dong Airport is just one of the airports in Shanghai. If you're not set on a specific airport, try changing your search from Shanghai Pu Dong Airport to Shanghai to see a broader range of flights – they might be cheaper.
During this peak season, accommodation prices often increase too, so it's best to book early. Or you could keep your fingers crossed and hold out for a last-minute deal.