Just an idea. This worked for me once when I had to attract the attention of a celebrity to setup a meeting.
To raise the profile of the petition we could ask someone like Ricky Gervais, who has a lot of followers and seems to have sympathy, to tweet it.
It works simply, as many people as possible with a Twitter account tweet this:
@rickygervais Ricky could you highlight this REALLY important petition for women's rights please: petition.parliament.uk/petitions/214118
It works best if the tweets are all sent at the same time as then the person in question is more likely to notice them (they'll be inundated with tweets and mostly they'll miss things)
If we do this, he may tweet it to his followers and it might get a really good response.
It worked when I used it for my campaign.