Whenever I try to drop caffeine, I get an unshakable headache. I'm not an FSD'er (as yet) and honestly, the caffeine bit is partly what's kept me from trying it so far. I get a caffeine headache by noon, and like you, the only thing that helps is sleeping. Sadly, noon means I have 5 more hours to go at work, so sleeping is not an option, and drafting leases with a pounding headache for a week before my caffeine addiction calms is not something I'm looking forward to
What helps me (minor help, but help nonetheless) is preemptively taking two or three aspirin (my roommate reports naproxen (Brand name is Aleve) works better, but Im allergic to it) a few hours before the headache normally hits.
I hope it gets better for you!!