You got an answer for everything. He hasn't told me how big to make my fermenter yet.
I think you should make it as big as you like.
You've got the 60 degree angle for the cone, which I think is a good idea. You've got to figure out the height and width constraints and use that as your guide. But if you're looking for a number, I wouldn't go less than 18" wide just for the stability. I would probably do 20".
If you have a cone that is 18" at the top, it will hold 5.7 gallons. The cylinder on top, 18" across and 12" high would hold another 13.2 gallons. So if my math is right you've got 18.9 gallons, which is in your 15-20 gallon range. I think there's enough space on a 4'x8' sheet to lay that out, but I could be wrong. Figuring out the geometry of a cone laid flat is more geometry than I want to do right now.