Very annoying having to overnight in Istanbul, but I don't think that the petition will have any impact this year. All the slots will have been allocated to the airlines by now and unless a pemanent slot becomes available (which will only be if an airline cancels a route into the UK) then they wouldn't be able to change it even if they wanted to.
The airlines apply for their slots in advance and don't always get what they want, but they also choose slot times according to cost as peak times are more expensive. The petition may well make the airline realise that they would get more traffic from provincial Turkish airports into the UK if they connected, so it could help for next year.
I had to book Pegasus into Stansted, but unfortunately they don't fly to the northern airports
