Ana, I'd say your piggy bank approach is the best. In the meantime, I'd just start doing your research. There aren't as many off-the-rack options in ti and steel, but there any number of really great builders who could build your dream bike, perhaps for less than you think (especially if you go with steel).

I just got a new (ti) bike of my own. Like you, I saved for it. It was still hard to swallow the cost, but I'm pretty sure it will be worth it. I pulled the trigger when I felt reasonably sure I had enough extra money that I wouldn't miss the money too terribly.