Perhaps the middle ground could be that the petition would still be available on the website and available for somebody to adopt, as opposed to automatically carrying over. I don't think it would require any rule changes to do that.
Is that something that you could do without a rule change? The website could simply say, “These are orphan petitions because Parliament dissolved. If you'd like to claim one of them as opposed to starting it afresh”—because it's already been translated and things—“click here”.