I think that was a great way of summarizing things, although I would caution you about drawing harsh lines between those different classifications.
If we read
"being tickled causes people to laugh"
vs.
"being tickled can cause people to laugh"
I'm not sure if there's any real difference there that we would care about on LSAT.
But I agree, the first version sounds like a conditional statement. "Being tickled" is sufficient to cause "laughter".
The second version sounds more wishy-washy. It's still compatible with the idea that every time someone is tickled he/she laughs, but it doesn't seem to guarantee that.
We might think of the first version as "All/always" and the second version as "some/at least once". And if you know your quantity terms, you know "some" is compatible with "all".
The distinction you drew for "contribute" sounds pretty appropriate. It seems like "contribute" is normally used with a more complex effect like obesity, cancer, heart disease, success.
Whereas, it sounds weird to say "being tickled contributes to laughing", since we tend to think of laughter as having only one cause in each instance.
For the sake of LSAT, I think we just want to know that words like "contribute"/"influence"/"affect" convey the idea of causality.
But you're probably correct in saying that LSAT only uses those types of words for complex things that may be the result of a "mosaic" of causes.
You sound like you're going to be a good lawyer.