Possible options for China trip

To Whom It May Concern,

Firstly, compliments for your website. Is very helpful for all the tourists that are planning to visit China.

I’m an Italian nationality and currently I’m living in Taiwan. I would like to visit China at the end of April with the target of travel in about ~8 days between Shanghai, Beijing and Great Wall.
Unfortunately, as Italian in Taiwan the expenses to get a touristic visa from here are very high (almost 200€ with agencies) and I would like to consider different options.
Option N.1: Use transit visa

Flight Taipei - Shanghai - Seoul
Stay 3 days in Shanghai

Flight Seoul - Beijing - Taipei
Stay 4 days in Beijing.

Would it be possible in terms of transit visa regulations, right?

Option N.2

Fly to Seoul, request a touristic visa to the Chinese embassy, fly to Beijing and travel via train to Shanghai.
My only concern is, as I’m not resident in Korea, can I still request a touristic L from there as an Italian living in Taiwan?

Many Thanks and keep up with the amazing webesite!