To be honest, I'm surprised and disappointed about the lack of response to this.
All the ingenuity and imagination that posters apply to abtruse cosmological Qs, and you can't think of one - not one! - idea that could help this problem.
I know that NASA aren't reallly asking for ideas, but then they're not asking for your views on......eg the nature of Phobos, either.

John
PS Sorry, Rb had a idea, but I think it was tounge in cheek