Are you recently back on the bike after a long time away?
(I have neck pain the first 3-4 rides of the season)
You say you have many spacers. How about you do it gradually. Don't remove them all at once.
Check that your seat is in the correct forward/back position (string+weight hanging from kneecap intersect the pedal axle when crank is in it's forward horizontal position)
You say you're flexible. Can you reach the floor bending forward with straight legs?
If you recently changed riding clothes the neck pain can occur. I use in cold weather a less ideal upper layer that constricts my neck a bit (adds pressure at the back of the neck). It's a tradeoff. I'd rather not catch a cold.
I have recently lowered my bars a lot. My tops are lower than all my friends drops!!! I can do it because I stretch a lot to feel comfortable in that position. Aero is a nice benefit...
I've been on my trainer through the winter. And yes I can reach the floor with my palms keeping legs straight. I do have short legs though.
What I'm not understanding is how I can go any lower. My seat height is fine, so the only 2 variables left seem to be reach and height of handlebars.
Currently when I'm on the hoods, my arms are almost fully extended with a micro elbow bend. I can move into an aggressive position and hold it for maybe 20 mins (flat back, elbows almost at 90 degrees).
But since my arms are already almost fully extended, how is it possible to move the bars any lower? Maybe if I bring in the reach? Not sure if that's the right way to think about it.