Maybe some kind of hindsight bias is at work, but I think I would have found Statement 2' a lot less crazy than Statement 2: the latter requires there being several billion male prostitutes, which (assuming that less than 20% of all males will be prostitutes and about 50% of all people will be male) would require a world population of several tens of billions.
(One of the main reasons why I would've found Statement 1' very unlikely is the “exactly 670616629.2” part, but I'm sure that was not your point: I'm sure you would assign a much lower prior to “I (army1987) generated a random 32-bit number a few minutes ago and it was 735,416,352” than to “... and it was more than 1 billion”, but you won't be shocked to know only the former is true. So I'll pretend it said “between 600 and 700 million miles per hour” instead.) I think I would've found Statement 1 crazier than 1', too: the idea that one particular colour (within the convex hull of the set of all colours I've seen before) has quasi-magical powers but an ever-so-slightly bluer or greener one has no weird properties at all sounds pretty bizarre to me (and possibly unfalsifiable, if there exist infinitely many colours), in a way that the idea that there is a speed (several orders of magnitude larger than anybody ever experienced) such that weirder and weirder things happen the closest you get to it wouldn't.
Statement 2 is more plausible than you think. Given the stated sizes of the spheres, it's highly unlikely that they exist solely as prostitute storage units. I'd suggest that they're aerial habitats, and prostitutes are just one of their many exports to the surface. They also offer really awesome bungee rides.
Alternatively, they could be organism production facilities, and the prostitutes are produced on site upon being ordered. They also offer pet velociraptors and colorful ponies.
Suppose I told you that I knew for a fact that the following statements were true:
You’d think I was crazy, right?
Now suppose it were the year 1901, and you had to choose between believing those statements I have just offered, and believing statements like the following:
Based on a comment of Robin Hanson’s: “I wonder if one could describe in enough detail a fictional story of an alternative reality, a reality that our ancestors could not distinguish from the truth, in order to make it very clear how surprising the truth turned out to be.”1
1Source: http://lesswrong.com/lw/j0/making_history_available/ewg.