That’s a big range of heights… it’s from a big mountain and a deep sea, to compare this to typical in-game heights - the highest mountain in Skyrim is about 627 meters… but then again, maybe you’re counting in feet?
If negative numbers are a problem then move them from [-2000,2000] to [0,4000] and move the terrain -2000 units down 
Anyway - you should be using a 16-bit png file and probably the new Shader Terrain Mesh system New terrain system - please test! or a custom tessellation shader (they are simpler then they look, there should be some example on the fora here)
For a big terrain an egg file is a very bad idea, it will be probably several GB large and it will take a looong time to load, even converted to bam it will be big.