144 hour visa free transit

No, unfortunately, you cannot do that. That would be e breach of 144 hour visa free transit rule and you are advised not to do that. You should proceed in exactly that way as you have reported at the 144 hour visa free transit counter. In other words, your next flight should be one for Taipei. Also, your planned return to Tokyo via Seoul would be a technical breach of the rule because the rule clearly asks for immediate points before and after your mainland Chinese stop to be in two different countries or eligible territories. As you can see, your alternative return trip has both immediate points in South Korea. I am sorry, but you are advised to wait for your flight to Taipei.