If I had to do a stain grade piece, I'd just build a seperate drawer box and front, like on a kitchen cabinet. Stain and spray the front, then attach to the box. Yes, it is not as refined as an integral front, but it is stain grade red oak.
If you are spraying a precat just spray the interior of the drawers once its assembled. Its quick and easy. I've done it and haven't had problems with odours. Just needs to off gas a bit before you put clothes in it
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