I don't think they ever did the double flip up thing on the wood or composite slat genesis. They did the double flip up on the next version (what my dad and I call the new old style) with the solid composite grey tables. The reason is that if you look at the grill, the bar that connects the front and back legs on the left hand side of the grill (where the flip up is) is how the flip up works in the wood version. The table hangs from a bar connecting the frame to the tab hanging below the end cap on the side, and then also has a bar near the bottom of the table with a slider that goes along that front to back bar. The notch at the front to back bar is where the slider slips into which locks the table in flip up mode.
On the newer composite ones, they redesigned it so that the edge of the table has a metal knobby disc that slides into a little bracket to lock it into place.
If you had an extra front to back bar/bracket to bolt in, and made sure that your propane hose didn't get in the way, I'm reasonably sure you could frankenstein something up. But I don't think one ever came from the factory like that (although I do learn something new about Webers seemingly daily)