Hey Signe, Thank you for a great witeup!
I work on a public transportation ticket app as well and I found your article insightfull.
I think you are right on the money focusing on the single most important action — purchasing a ticket as quick as possible.
We are constantly monitoring this specific process in various situations — first time user, registered user, user with saved credit card etc. and I am proud to say we managed to get it to a mere 7 seconds.