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I was able to find a shalwar kameez outfit (not quite the payraan tunbaan, but close enough for quick and informal impression purposes) going to a Value Village. Amusingly (and somewhat ignorantly), the Value Village management at the outlet I went to hung shalwar kameez(es) in the "Men's Pyjamas" section.
So, if you're looking for something similar to what I found, go to a Value Village and look in the men's pyjamas section. I actually found a number of them that worked perfectly.