Kinda the same, trying to grab that SR and loosing hope at it...

My 4 tries of the day (runing out of gaz) was the R girl, 3 time, on a 1:30 or 2:00 timer, and once the N girl after a 2:00 timer.

Also, about EX wild card,"An item that lets you increase any card's Ex Level by one.". "If you clear a One-Shot Mission's corresponding mission, your Ex Level limit will increase.
After an Ex Level limit is unlocked, you can raise all your cards to the upper limit."
Quoting from the FAQ, card page.