Vancouver - Taipei - Hong Kong - Shanghai - Vancouver

Hi, my family and I (2 adults + 12 yo child) are going to have a tour as above in June. The schedule will be,

YVR - TPE : June 9 (4N in Taipei)
TPE - HKG : June 13 (5N in Hong Kong)
HKG - PVG : June 18 (4N in Shanghai)
PVG - YVR : June 22

Understand from the consular websites of these 3 countries,
- Taiwan - seems we should apply Taiwan visa thru' local travel agent here.
- Hong Kong - visa is not required for tourists to 180 days; it's granted according to nationality.
- Shanghai ROC - we also need to ask the local agents for our visa.

Since we book our tickets & hotel online, is there any simpler way to apply our visa to Shanghai, i.e. thru' official formal visa consular or online application, rather than asking us to go to the travel agent. The agent will charge us for their administration service. Or maybe we are eligible for "144th visa free" as well. If so, how could we get the confirmation about it?

Thank you so much for your attention.