I have an odd way of setting up, but it works really well for me, so might be worth a try.
I get down and grip the bar, set foot position etc.
Tip forward onto my toes, which extends my torso and hips slightly; this allows me to suck in a big breath just as well as if i was standing up.
Then sit back into position on my heels, pull myself down to the bar and pull as usual.
So far I haven't come across many lifters who set up similarly to myself (in terms of when they take their breath).
However, I always lift beltless (I'm thinking this setup may not be possible with a belt?), simply because I never got into using one and am now very comfortable pulling and squatting without.
This may not apply to you OP, but it might be worth giving it a try in the scheme of things to see if it works for you!