What you describe is exactly what my Celeste trees did last year when it was hot and very dry. The fruit went from darker green, to a light green and then, they dropped. Not all of them, but many (Too many) of them did that. They would also feel lighter than the darker green figs, not as solid. I was told by an orchard lady to start watering them before they fruit, on a regular basis, unless it was rainy, of course, and keep that up through the fruiting season. She had an over head watering system. I think that may have helped to cool the leaves and maybe "fake" the trees into thinking it was raining, since the water was falling on them like rain. Don't know for sure, but she said the Celestes didn't drop as many figs if they had steady watering. She told me 2-3 hours every other day. This year, I've tried to keep the water to them, but not from overhead, and so far, they look good still. Time will tell. I was putting way too little water on them last year, though.
Are your Celeste trees mulched? That's a must, as well. It sounds like you are using a lot of fertilizer. I don't know if it is too much, maybe. Also, did you see if your soil needs lime? I've been told that if the trees need lime, it can make them drop fruit, as well. Other trace nutrients, as well.
I put fruit tree stakes around my Celestes this year and they have gone and lost their minds and are growing all over the place. I don' tank I'll do dat again, no! :)
I put one stake for each of the four trunks and maybe that was too much, but they're both loaded with figs.
Did you look for evidence of nematodes? Is your soil sandy? Did you put lots of organic matter in the planting hole when you planted your tree?
I hope things improve for you with the tree and maybe someone else can help you out with this problem.
Celestes are survivors and if they get hot and dry, will jettison fruit to take the stress off of themselves. I wish I could get cuttings from someone who has a Celeste that does not drop friut, but those trees seem to be rare, if nonexistant. :(