I purchased spring-loaded drawer dividers and mounted them against the side of several drawers in my bathroom (I added double-sided foam tape to the ends to secure the divider), and then was able to set this tray on top of the divider so it would slide forward or backward using the edges of the trays as glides and the edge of the drawer on one side and the spring-loaded divider on the other side to support the trays.

I added adjustable bamboo dividers underneath to keep other items sorted.