I sided with the Templars and couldn't initiate Last Resort of Good Men, either, because the cutscene where Dorian receives the letter about Felix was never triggered so I thought I was doomed and had to start over, but after mucking around for about seven hours, I found a solution that worked for me.
What did it for me was NOT finishing One Less Venatori. I only finished it up to 2/3 (I didn't kill the group in Exalted Plains) and then went back to Skyhold to speak to Dorian. Up until that point, I had exhausted all dialogue with him and flirted with him at every opportunity I got. With One Less Venatori only up to 2/3, the cutscene with Felix' letter did trigger for me and Mother Giselle was in the hall after that with the letter from Dorian's father. So I guess for me that last Greatly Approves pushed Dorian's approval of me over so I couldn't start the quest.
I don't know if I was just very lucky or if it's an actual solution, but I thought I'd share anyway in case it works for anyone else. Good luck!
EDIT: I.... just saw someone else posted a similar solution. Guess that's what you get for not reading the entire thread, oops. Oh well 😛