The south west lakes trust rules actually state that two kitesurfers are allowed on there lakes at any one time! So, officially, kitesurfing IS allowed. However, if you call any of the lakes, the staff will tell you otherwise. I would suggest turning up with a copy of the rules and pointing out to the staff at the centre that their own rules state that you can fly. They'll probably try and charge you a launch fee but its gotta be worth a go!!
Stithians might be the better option as Siblyback gets V gust and isn't as big!