Baby sleeping through the night but boobs are getting engorged

My baby is 15 weeks old and has recently started sleeping from about 8:00 p.m. to 6:00 a.m. without waking to feed. 🎉
The problem is that my boobs don’t seem to have gotten the memo yet.
For context, I exclusively pumped for her first 7 weeks, so my body got very used to overnight milk removal. Over the last couple of weeks, I’ve gradually reduced overnight pumping. Right now I still get up once overnight, but only pump for about 5 minutes just enough to take the edge off when I’m feeling really engorged.

I’m wondering what others did when their baby started sleeping through the night:
Did you gradually wean the overnight pump completely?
How long did it take for your body to adjust?
Did dropping the night pump affect your overall supply?
Any tips for dealing with the rock-hard, uncomfortable boobs while transitioning?

I’d love to sleep through the night myself, but right now the engorgement wakes me up before my baby does.
Would appreciate hearing others’ experiences!