I won't argue that it's not cool - it is
However, I think you missed an important part of the debate here. Specifically, this:
To reiterate, in order to end your move action mid-air with the Athletics skill, you must be taking a double move action. A double move action requires that both move actions be the same. Since Fey Step isn't at-will, this isn't possible.
Therefore, you must take your move action to run up and high jump, then sub your standard for the move action in order to Fey Step. However, you're trying to end your jump in mid-air, in which case the skill specifically states that you fall prone - before you get to Fey Step. Which means you're back to square 1.
Likewise, trying to ready an action to Fey Step when you reach the apex of your jump doesn't work. A readied action is an immediate reaction, which you can't take on your turn. Even if you declare that your turn ends at the apex of your jump so that you can use your readied action immediately after your turn but before the next character's turn, that means you are still ending your move action mid-air, which means you fall prone. Back to square 1 again.
Personally, I'd probably allow it in my game. But you asked whether the RAW support this, which I really don't think they do. Try something like the other party members throwing the eladrin in the air - readied action should work then, since it's not his turn, and I'm sure there's no rules about how throwing another character in the air works, so that's up to your DM how it works - even then, readied actions can interrupt other actions, especially movement-oriented ones. Also, a githyanki readying an action to use their racial power when an ally jumps should be just fine, RAW.