//Maybe it would deter said extremists from beginning a petition if they were made to pay, say, 25% of the total cost of another election if the MP is re-elected.//
It might, but then it just seems pointless to effectively restrict this privilege to people who can afford to run 25% of an election campaign. Not terribly democratic.
The solution is to have fairer elections in general, this is a pointless measure that will almost certainly get pounced on by well-organised extremists.