There is already a fat woman on kilamanjaro and the summit in Russia is mostly a train ride. That's 2 of the 7 right there.
There's Mt Harney in SD. Plenty of walk up 14k s in CO that she could drive up and snap a selfie at the peak.
https://www.amazon.com/dp/B00QW7VB1M/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1