The endurance levels are sort of a throwback to the original "eat 'em up" game Shark Shark. So they are supposed to be really challenging. And the third endurance level is particularly hard. Probably the hardest in the game.
I think that your strategy of staying in the middle of the level is good - it gives you more directions to run if an amoeba comes after you. I can't say there are too many other tips... it's really a question of endurance
. Let's see... If your hand is getting tired, you could pause the game (space bar) and rest for a bit, or you could use the arrow keys instead of the mouse. One thing that might help is to turn the "Grey Goo Speed" all the way up in the options menu. This will make the grey goo respond more quickly to your mouse movements.
You could try playing really conservatively. By that I mean don't go chasing after really tiny superclusers, just go for the ones that are closer to your own size (and will therefor have a greater growth effect on you).
If you get Gravity Well cheat and turn it on, the game won't save any progress that you make. Same with any cheat that actually helps you. Purely cosmetic cheats like the rainbow goo still allow you to progress. The cheats are just to play around with, they won't help you get higher medals.