Thanks for your efforts, which were not small! However, I could not find the rule you posted in an older thread on the Q&A section of the current website, although my Chinese is not good, so maybe I missed it.
The offer I want is available online only, which means the foreign ARC numbers are not accepted by the system.
How to crack this nut? It will require need someone with enough authority to issue this online offer “manually” or even better, override the setting for the Taiwan only ID number format to include foreign ARC holders.