Impossible just using keyboard controls. In fact I think I soft-locked it by going tot he right from the beginning... can't fall through platform. I thought I tried everything, but you have to hit "S" + "Space". Game's still hard as hell the way the controls are. You'd have to memorize where all the zombies are. Edit again: memorization won't even help, because there's a megazombie downstairs of the burning houses who takes more than two shots and who can't be shot from the perch and rips you to shreds. So.
Much, much better. It's mostly about being able to move just slightly faster than them so you can stop and reload. I was actually able to make it to the end of level 1 and see all the cool stuff you put in there (the pools of blood are a nice touch).
My main problem this playthrough was not being able to do many inputs at once. For instance, I'd hit "right" to pull out my gun, hold it and then press and hold "down" to aim down, and then hit "S" to crouch, but then you can't fire the gun unless you release "right", which is a little unintuitive.