After doing some research, I see a pattern in the available office storage furniture and supplies. You are the "victim" of normal workflow. Your need is counter to the requirements of the general office furniture requirements.

There are myriad of accessories and supplies to convert general purpose filing cabinets from flat folders (and dividers) to hanging files. The bulk of filing cabinets that use hanging files have high sides, rails, or bars for supporting each side of the "hanging" file folder pocket. Alternately, low-sided drawers can be fitted with accessory rail kits.

As plain filing cabinets are more versatile, various kits are plentiful that can convert them for using hanging files. None that I could find go in the reverse direction—getting a special-purpose hanging file cabinet and trying to "dismantle and remove" the specific feature it was designed to accommodate.

What to do depends on what you want to store. You never said. Without modification, for example, you could probably put twenty or thirty collapsible music stands in one drawer. A number of different drawer organizers are available made from different materials from plastic, metal, cloth over a metal frame, fibreglass, or even baskets. They are all available in different sizes in hardware stores, apartment decor, or housewares specialty stores such as Ikea or StrucTube. There are organizers for art supplies which come in a variety of shapes and sizes that are chemically resistant. Last, but not least, office supply stores have containers suitable for vertical or horizontal storage of stuff. You can mix-n-match.

Do be aware that stationery and office supplies have their own "standard" sizes and formats. You, by going your own way trying to repurpose existing equipment, are "violating" an established standard for another which usually involves a hassle. You're discovering that.

There are components such as corners and sides that can be cut from thin wood and "clipped" together to form containers and other things for housing instruments, too, such as Playwood Connectors from places like "Lee Valley" for wood workers among others. (I don't know your budget limitations.) As well, most any shipping company can make or provide a container to fit your exact size requirements.

It's entirely possible there's an exact size to meet your needs under a different category from office filing system. You never mentioned the size you need or the number of containers. Be sure that when you do specify that metric as a "Do not exceed" measurement.