You mentioned in an earlier response that Tyrion didn’t really have an alternate path if he wanted to get out after Tywin vetoes the inheritance. But it seems like he was planning that anyways, in his last conversation with Sansa – talking about how it would be very wise for him to get as far away as possible from King’s Landing when Joffrey outgrows his regency, including to the Free Cities. What’s the difference, other than time?

Preparation. Tyrion would have needed to take a lot of money with him to the Free Cities. Also, there’s a difference between Tyrion leaving the family and breaking relations with Tywin and taking a diplomatic trip to the Free Cities to stay away from Joffrey. 

Tywin would probably have accepted the latter, certainly it would have made his job easier, and would have funded Tyrion in the style of a Lannister to avoid shaming the family name, etc.