My kitchen has drawers and doors. I've lived with it for 26 years. Every snack. Every meal. Every time I bake. Every time I put groceries away. Every time I put dishes away. Every time I get dishes out. Drawers and doors. A serious pain but stupid me allowed the woodworker to put the dratted doors on and now I'm stuck.
My considered recommendation: "no doors."
Now if I understand you, correctly, the drawers fill the entire inside of the cabinet. I like "2 for 1s." How about taking the doors off, getting rid of the door problem? A cutting surface, organization possibilities galore and NO DOORS.
I know it's possible to take doors off in a sewing room because I did. The old kitchen has 19 running feet of cabinets, top and bottom. They're doorless, top and bottom, and I've filled the shelves with folded fabric and see through plastic containers. Snitched DH's label maker and as I fill things, I label them.
When I'm sewing, nothing is neat.
Good luck with your organization. I love mine - in my sewing room.