Any reason you're avoiding Chinese carriers? The non-stop routes are split 50/50 between the Chinese and Taiwanese carriers so you're limiting your options right off the bat.

Unfortunately this route is always a little pricey in my experience, if anyone has any strategies to get a cheaper fare, I'd be interested.

The good thing is that you can now fly from Taipei-Songshan to Shanghai-Hongqiao non-stop, which is a vast improvement over the bad old days of transiting Hong Kong to get between the PRC and ROC.