I've been considering this data as well. Currently I have a scheduled cron job via the UTA API that parsers the output to PostgreSQL tables. I haven't yet pulled an extract using joins, but I suspect it might be complex. Just haven't had the time, or I would have used the sample-feed as a test first, but I had to prove out the connection ability (as a proof of concept). It's certainly interesting.
Could you want to post a screenshot to share with the community?
Considering the route optimization issue, have you looked at pgrouting yet - that's why I wanted to pull into Postgres/PostGIS.
Using your UTA example, the output would look like this, except the route lines would be dictated by the shapes.txt file in GTFS. I'm able to map the two sets (shapes.txt and stops.txt) separately so my goal is to combine those two datasets, hopefully without having to do complex joins. The real problem comes with Tableau's inability to be able to map more than one set of lat/long columns.
When I tried to match the two sets before, it was basically programmatically searching through the shapes.txt file for the closest match to the given stop's lat/long. For example, if the stop in stops.txt is located at (-27.503864,152.978714) and the two closest points in shapes.txt are (-27.5038623196,152.979583709) and (-27.5038008005,152.978722116) then the accuracy is (0.0000016804, 0.000869709) and (0.0000631995, 0.000008116), respectively. These numbers vary widely so it's difficult to go about it this way.
I'm hoping someone from Tableau can chime in as to whether this is built in or not. I know it wasn't in Tableau 7 but I'm not sure if it's in Tableau 8.
What do your PostegreSQL tables look like?
In all honesty I just haven't had time to look, but when I had to do this for the Utah State University Fire and Police viz (two separate lat/longs) we did a left outer join to get one set of lat/longs. I suspect it will either be the same again, or a union. I'm busy doing other stuff for the University, department summary dashboards; and it's the first week back for students, so things are hectic, to say the least!
Keep us updated, this has the makings of a very exciting project...