Problem with Maya to Unity Animation

First I preface this by saying I'm an absolute beginner - sorry if I ask any silly questions!

So I've been working on a character in maya with some basic animations (idle, walk, run, etc.) just so I can mess around with character controller in unity.
The animations look fine in maya, but when I try importing them into unity, they go berserk - here's an example:



As I said, that twitchiness with the front half of the body wasn't there at all in the maya file, and its even worse in the walk/run cycles.
In terms of what I've done, I tried both importing the maya file directly into unity, as well as exporting it as an fbx and importing that. I also tried manually baking the animation with edit>keys>bake simulation in maya, but I still get weirdness in the animation when i import it to unity.

I'm not the most proficient rigger (I freakin suck at it,) so I thought my shonky rigging job might have something to do with why this is happening, but surely that wouldn't affect anything if the animation has been baked, right?

Any help at all would be greatly appreciated!

Thanks!