Hong Kong/Macau/Taiwanese do not need any local spouse to stay and work in Shanghai, hence they cannot be applicants by design. The regulation I provided you with applies to foreigners only.
Let me walk you through the Chinese regulation. 探望 is formal Chinese for “wishing to join/visit.” 被探望人 means “the person being visited/joined.” With your understanding of Chinese I am not surprised that your efforts have thus far proven futile. And your case once more shows that a Taiwanese wife is not necessarily a great help when dealing with authorities.
（二）办事的手续 Application Procedure
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6.提交与申请人身份和事由相符的证明材料 Supporting documents depending on the applicant’s situation and purpose:
（1）探望本市居民，须提供被探望人的本市常住户籍证明和居民身份证的原件及复印件；For joining citizens of this municipality, provide ID card as well as household registration of the person you join
（2）探望外省市居民，须提供被探望人的中国居民身份证、有效的居住证和本市单位在职证明或本市房产证的原件及复印件； For joining citizens of other provinces, provide ID card, residence permit, as well as work place certificate of the person you join
（3）探望华侨、港澳台居民，须提供他们的身份证件及在沪6个月以上的常住证明原件及复印件；For joining overseas Chinese and Hong Kong/Macao/Taiwan residents, provide the respective ID card and certificates documenting residence in Shanghai municipality for 6 months or more of the person you join
（4）探望常住外国人，须提供被探望人的《外国人永久居留证》原件及复印件。
注：To join foreigners, provide the original of the “Permanent Residence Certificate for Foreigners” as well as a copy thereof of the person you join
In conclusion, the requirements for foreign spouses of Taiwanese are quite generous in comparison to non-local Mainland Chinese as well as foreigners. Whereas the former need to document the employment of their Chinese spouse, this is not required for foreign spouses of Taiwanese. Furthermore, foreign spouses of Taiwanese receive far better treatment than foreign spouses of foreign permanent residents. Not even to mention the foreign spouses of foreign residents without a permanent resident certificate. From an analysis of the relevant procedure, we can see that foreign spouses of Taiwanese receive treatment somewhere slightly below foreign spouses with local Shanghai spouses. Therefore, the treatment of Taiwanese in Mainland China is hardly comparable to that of foreigners.