You know, that almost would work: Gary Seven's bosses seem to know what's going to happen or what's best for humanity. Maybe it's because they've seen the whole timeline and are making tiny corrective edits.
Someone like the Doctor could be a part of the plan, a fly in the ointment or maybe in the end the architect of the whole thing!
And as to the BSG crossover...I started a thread awhile back about what Galactica will find when it reaches Earth....and a few people said Trek-Earth!!
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth