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I've found a solution to my issue, though I'm ashamed to say I didn't find it sooner. It's not an obvious solution, but it is provided under "Possible Issues" in the GeoGraphics Mathematica 10 documentation. To combine polygons: multipoly =...
This seems like the best possible answer to me. Makes the joke funnier, really: We had all been assuming someone had merely added a sign reading "Space", rather than defacing an existing sigh. Well done, Hans.
Well, I'm not sure why that wasn't working for me before, but I got it working by upgrading from 9.0.0 to 9.0.1. It seems like a weird thing to be broken by missing that upgrade, but it fixed it.