“If a character deliberately jumps instead of merely slipping or falling,”
I don’t think this means that a character can’t deliberately move into a position that results in a fall – falling is not defined as only accidental here. So, I think a character can five foot step into a space that results in a fall, with the appropriate damage as listed.
Whether they can do anything on the way down depends to me on how much of their turn the fall takes up. Someone falling for a full six seconds could indeed take some action, I think.
What if they take the time for a full attack before the step, though – how much time would they actually spend falling that round?
In the example, I think it is pretty simple: a character so few feet up would step off and hit the ground in a matter of an instant, with virtually no possibility of doing anything on the way down. They would face AoOs from any whose threatened space (vertical or horizontal) they left in the course of falling, and end prone and slightly injured. They would still have their turn other than the step at that point, however, and could use a move action to stand up (taking relevant AoOs), and make a single attack.
The much better alternative is clearly taking the full attack, and then stepping and falling, ending their round prone.
Taking a full attack during such a very short fall is not so much cinematic to me as cartoonish. Just doesn’t do it for me. Someone who is falling a substantial distance, for sure, that would be cool. As a DM, I would tend to make this attempt turn out comically, rather than anything else – it is just too much of a stretch, and while I applaud the general idea of heroic efforts, you have to try and let reality intrude a bit, I think. I would have the character hit the ground while attempting a full attack, and be able to stand and make a single attack.