Even if we discovered that the belts were 27 feet long, (note that the OP specified Hellcats), there are a couple of larger problems:
I cannot recall every reading a combat report, a biograpy, or a fictional tale (amny of which have been based on good research) that actually used the phrase. So where was the phrase hiding until it made it into print?
More importantly, what idiot pilot would ever invite the ridicule that the following statement would inspire?
Giving the enemy the “whole nine yards” implies that you are such a crummy shot that you wasted your entire load of ammunition trying to bring down a single plane. (And if you continued shooting into it after it was clearly damaged beyond repair, your CO was liable to take your head off for wasting ammo.) Japanese planes were not the heavily armored kites that Focke-Wulf cranked out. The Val and the Kate were pretty rugged, but the Zeke, the Nell, and the Betty were all fragile with a tendency to ignite. I doubt that you could actually put an entire load of ammo into most Japanese planes before they disintegrated.
@Bookkeeper
I think you might have misunderstood me. The ammo belt assembly came in a box. The maximum length of a belt assembled using all the parts would be exactly 27 feet long. The ground crew might or might not use all of it, or they might use more than one. The belt was assembled to the length required by each plane and gun. The only standardization was that each belt was a maximum of 27 feet long out of the box.
You are correct that the links were in fact ejected with the round, so they were never reused. After a mission, a new belt assembly (a maximum of exactly 27 feet long) was pulled out, filled to the correct length, and loaded into the plane for the next mission just like before. How many links/sections that were actually used were determined by the specifications of the plane.
@Tomndebb
My understanding is that you had a burst of 4-6 seconds in most planes. That was it. If you got the chance to empty the guns into a target, you did it. Kills weren’t automatic by any means. Unless the plane in front of you exploded, or the pilot bailed out, you kept firing.
As for the Zero being an easier mark, I passed your comments past the Navy Ace I mentioned. He said he emptied the guns on a target numerous times, only to see them fly away effectively unharmed. He said getting in a position to score the kill takes a little skill, but actually scoring the kill was always luck.
When I asked him how he managed to get lucky 12 times, he just smiled, and then looked down at his wheel chair. Needless to say, I dropped the subject of luck.