Need tips, approach, or method(s) to eliminate smell/odor in a closet short of a tear down?
Your closet is going to be considered a small enclosed area, a perfect description for a low-cost ion generator. They are frequently used to eradicate pet odors, smoking smells and even fire damage smells. A family member once sold tool-box sized devices and also rented them out for circumstances similar to yours. It was more of a whole-room device due to the size, power and volume of air moved.

You'd be able to get away with a smaller unit for the closet. A caution with the device is that people are to be vacated from the area being treated, not a problem for your closet troubles.

eBay and Amazon sell various devices. I'd consider even to use a motor vehicle sized device designed to plug into the accessory outlet formerly known as the lighter socket, if you wanted to save money or reduce the risk that it would not work as needed. Of course, with a tiny unit, you'd expect a longer period of recovery.

Using "ion generator" as search terms, many devices are returned with prices from the tens to hundreds of dollars. I would be suspicious of any device that does not specify that one should vacate the area, as that would be an indication that it produces low or insufficient levels of ions for your purpose.