As for how many 3-point building are needed to get to the cheetah level, I’ve done it in mountain, with 3 3-point buildings and 3 1-point buildings, and in gambling, with 10 2-point buildings and 1 1-point building. I wasn't sure 160 points would be possible without 3-point buildings, but it only took about an hour to reach 120 points on that project. It took a few more hours to get the last 40 points.
The key was stockpiling items ahead of the project, focusing on scarce and time consuming items. It helps to have enough for a couple of tasks on the really difficult items, even if that means you don't have room for some more common items. Also, at least 100k-110k simoleons. I focused on the higher point buildings, and the projects were completed in under 5 hours. (The mountain project would have taken longer without speed-up tokens, but still would have been complete in well under 24 hours.)