First, ESEE 3s and 4s are the same thickness, just different lengths by an inch.
Second, there is more to a "survival" knife than thickness. How about length, shape, thickness, and grind.
For your application, per what you listed in OG post, I should think you would like a 3/16 thickness. Here's the trouble, you want a skinner/food preper that is also good for bush-craft. Well, skinners usually have a blunt blade style with very little tip and are usually on the shorter side. Food prepers usually have a completely straight edge without any curve at all and a blunt like tip and are usually around 6 inches. Bush-craft blades are usually longer (say upwards from 7 inches), have a spear point or drop point, and have a thickness of 3/16 and thicker.
I guess I suggest a BK5 for you. I should think that knife will cover all of what you want to do.