For barretts, take some yarn, and make a thick braid to hang on the wall. Then, you just slide the barretts through some of the yarn.
For Headbands, hang a looped peice of ribbon on the wall, and just slide one side of the head band through it. If you have the cloth head bands, or big scrunchies, do the same, but use a safety pin to loop the ribbon, then just unpin it to pull one off.
For hair ties, small clips, little claws, etc, keep using the tackle box. But the above idea’s should give you some ways to get the larger items out of the box.
I use cookie jars, too. I find those square glass ones with the air tight suction lid. One for rubberbands, one for bows or ribbons, one for barretts, etc. My older daughter doesn’t let me do anything with her hair, but my younger daughter has highly unmanagable hair. We have to put it back in pony tails on the side or baretts, or it’s in her face.