I think a rocket and moon probe is a bit much to be sticking through a blind wormhole, have you looked at a NASA launch platform lately? Not to mention the timing problem, if you don’t know how far back the wormhole leads you don’t know how far away the moon is, so working out the thrust from orbit to make the slingshot is basically not possible. They might have a plothole there for your solution is much worse.
I’m not sure the probe really did much of anything, except count time. Also there’s indications that it really isn’t an alternate universe, but that it was just the line sold to people.
They can determine the distance using a conventional telescope and some math since we already know the actual size of the moon this should be child’s play, mathematically speaking. As for the rocket, they sent land vehicles through the rift, a rocket in sections would be able to make it through, some assembly required of course, but they are already sending smart people through.
Of course the moon should only be about 149KM closer to earth 85 million years ago. That is not that much further than it is now. (stupid first episode miscalculation).