I want to have a directional falloff effect like in the picture below, but so that the edge is not so uniform and has some "randomness" instead. I'm not asking for how to widen the width of the falloff, but rather how to make it so that some of the objects come down a bit earlier than others, while still preserving the overall directionality of the falloff.
Figured out the answer before posting the question :)
So what you can do is add a wiggle falloff node and mix it with the directional falloff ("add" mode). With the "evaluate falloff" node you can then convert the combined falloff to numbers that are easy to manipulate. The idea is to clamp the resulting falloff so that the top&bottom remain flat, but just the middle is randomized. Then just convert the strengths back to a falloff with the custom falloff node.
It takes some tweaking of the values to get it line up right, but the idea is quite simple. You can see the exact values I used in the screenshot below.
I also added a "map range" node after the clamping, to restore the upper and lower limits to what they should be according to the offset matrix node. (they shift a bit as a result of the clamping)
Hope this helps somebody!