Yeah, I do that too. If they still get stuck, just run into them until someone finally jumps up.
2 strikes a better balance between frustrating and too easy. Survivor AI isn't dogshit, for one thing. At the start of both games, you'll have a hard time actually keeping up with the timer. As you level up, they both become considerably easier, though the original still has that awful AI that you have to put up with. I do prefer not having any emphasis on combo weapons in 1 though. Plus, better protagonist.
Regarding platinum, prepare for mind-numbing repetition. Mainly because of the trophies where you have to kill tens of thousands of zombies in a single playthrough, so you have to spend hours driving a car around and mowing down zombies. Which sounds fun, but quickly becomes dull.