But I just found this one, and the more I think about my situation, the more I think it qualifies:
http://www.amazon.com/Lenovo-21-5-Inch-Touchscreen-Desktop-Aluminum/dp/B00CG8K2YS/ref=lp_7226404011_1_9?s=pc&ie=UTF8&qid=1387903856&sr=1-9
Very nice. I’ll bet that sucker runs hot.