You could line the walls of the closet before the organizer is installed with something like this:

Here is a link that might be useful: cedar liners for closets

I put some cedar behind some of my sweater shelves. I will tell you that some of my sweaters have had holes over the last summer. Your option sounds like you will have more cedar so maybe it will work.

A little aromatic cedar goes a long way as far as moths are concerned. There's no need for every surface to be covered by it.

In fact, you DON'T want every surface covered, the aromatic cedar oils can spot some fabrics if they come in contact with the wood. You want just enough cedar to emit a mild odor (and remember it will need to be sanded lightly every year). It is more important to have the closet airtight [bugproof] when it is closed. While cedar and similar strong scents deter some moths, the only way to be positive the fabrics are safe is to store the clothing in an airtight container and never ever leave it open.

The aroma of cedar is supposed to disguise the smell of wool and other animal based fabrics so the moths won't lay their eggs in it and some versions of it might actually kill the larvae (which might have already been in the clothing when it was stored) but in general this is not a very effective way to protect your clothes.

If you go the cedar route you should use as much Juniperus virginiana (Eastern Red Cedar, Eastern Juniper, Red Juniper, and Pencil Cedar) as possible but be aware that it will lose its effectiveness as the oils dry out. Perhaps it's possible to buy the oil extract in a form that can be replaced.