Yes, they started filming in early Oct., but TH and EO had been together in Nashville (at some point and for some amount of time). Remember RC when he wrote about all the work TH was doing to prepare for the role? He said that he'd seen him (TH) rehearsing lines with his leading lady for six hours straight.
I thought that MA divorced at the end of 2013/start of 2014. I don't remember where I read that. He was married as late as 2012 when he mentioned speaking to his wife about TH.