Ah, I didn't consider depth. Looking at the options on Amazon, they would be too thick as well. Nevermind then. https://www.amazon.com/dp/B00MO818IY
They make outlets that are DIN-rail mounted. https://www.amazon.com/IMACP01-Grounded-Receptacle-Mounted-Convenience/dp/B00MO818IY/ref=sr_1_1?ie=UTF8&qid=1500411599&sr=8-1&keywords=din+rail+mounted