Yeah, I would do the same thing! I wouldn't need the added drawers & mine wouldn't be as tall.
I wasn't thinking of actual individual drawers, more like shelves/trays that would hold the organizers. I saw this type of set-up with slides that looks like it would work good. The HF organizers have a recessed area in-between two tabs that allows a thin piece or wood to be used to locate the container.
IMG_0398 2 .jpg
Storage Container With Slides .jpg
The added cost of the drawer slides is a concern, But as you pointed out! Maybe a combination of the two styles, slides on the upper section & pull-out slots for the lower section?
Doug