I used to use the the Fighter Organization window, too. However, after some experimentation with the Naval Organization tab of the Task Groups window, I have completely abandoned the Fighter Organization window. As Steve points out, it really is a "one-click" operation, once you've set up your organizational structure. Here's what I do:
(1) Organizational set-up:
Create a sub-branch of the carrier task group containing just the carriers themselves. (This is not strictly necessary, but it helps keep large task groups organized. ) Within the carrier branch, create a sub-branch that will eventually include all of the carrier's fighters--think of this as the "umbrella branch". Within the umbrella branch, create individual sub-branches for each carrier, that will contain only that carrier's fighters--the "squadron branches". (At this point, the umbrella and squadron branches will be completely empty--they are just placeholders on the fleet organizational chart. )
(2) Initial fighter assignments:
(a) Once the fighters are built, go to the Task Group Window, select the Naval Organization tab, and in the branch window, choose the squadron to which the fighters will be assigned. Then, in the top window, select the TG that currently contains the newly-built fighters. (By default, this will be "New Fighters". ) Using the "Add Ship" or "Add TG" button (second set of organizational buttons), add all of the desired fighters to the chosen squadron in the branch window.
(b) Now, with the squadron branch selected, "Add" that branch to the Stored Branch List (bottom set of organizational buttons). Make sure to "Clear" any prior stored branches! Next, in the branch window, select the specific carrier that will be the mothership, and then click the "Assign MS" button (second set of organizational buttons). Finally, reselect the the squadron branch, and click the "Land Branch" button (third set of organizational buttons). Voila! Your fighters have landed on their carrier, and have been transferred from the construction TG to the mothership's TG.
(3) Launching parasites:
(a) To launch an individual fighter squadron, select its branch in the organization window, and click the "Branch Only" button. You now have a separate TG containing the fighters, with a TG name identical to the squadron name from the branch window.
(b) To launch all carriers' fighters into a single TG, select the umbrella branch that has all of the squadron sub-branches, and click the "Branch + Sub" button. You'll get a TG with the name of the umbrella branch, containing all fighters from all squadrons.
Also, note that this system works for any parasite-mothership configuration, not just fighters. It works for FACs and FAC carriers, for survey/scout carriers with multiple larger-than-FAC vessels, and for "leviathan" jump-carriers that haul one or more full-fledged fleet combat vessels--these are all assignments that cannot be made through the Fighter Organization window.
As an added bonus, it is also a lot easier to reassign fighter squadrons using the Naval Organization tab. For example, when a new generation of fighter becomes available, I typically consign the older models to my "colonial defense fleet", assigning them to a fighter-base PDC somewhere. I fly the carrier to the colony, and rename its fighter branch from, say, "Apache Squadron 001" to "Colonial Squadron 015". I then use the organizational buttons to Store that squadron, select the branch containing the fighter-PDC, then Move the squadron, and finally use (2b) above to assign the squadron to the PDC and land them. I then create a new (empty) fighter branch for the carrier, ready to accept the top-of-the-line fighters once it returns to base.
