Your answer can be found in section 3.2 on the Diccionario panhispánico de dudas. Below is a translation of the original text:
3.2. One adjective postposed to several nouns. When one adjective qualifies two or more coordinated nouns and is postposed to them, it is advisable to inflect it in plural and masculine if the two adjectives are of different gender: «Tiene el pelo y la barba enmarañados»1 (Matos Noche [Cuba 2002]); «Apareció [...] vestida con traje y mantilla blancos»2 (Hernández Secreter [Esp. 1995]). If the adjective agreed only with the second noun, there could arise some ambiguity because it would be possible to interpret that the adjective only applies to the nearest noun: vestida con traje y mantilla blanca (where both the suit and the mantille white or just the latter?). However, when both nouns are considered to form a unit of which each is only a part, the adjective can agree with the nearest one: «La gente de origen y habla francesa predomina en la provincia de Quebec»3 (Tiempo [Col.] 1.7.98).
To answer your question, taiwaneses is the right choice. If you are concerned about the cacophony of an adjective following a noun with which it doesn't agree, you can always change the order of the nouns so the masculine goes at the end, as proposed in the comments. That isn't necessary, though -- to me, taiwaneses sounds just fine in your sentence!
Interestingly, the rules change if the adjective is preposed to the nouns; in that case, the adjective must agree in gender and number with the first noun (La indispensable vigilancia y control nocturnos), except when qualifying people (los simpáticos Paco y Toni). When the conjunction used is o instead of y, the rules are similar to the ones mentioned for y:
Cada vez que mueren un hombre o una mujer viejos [...],toda una biblioteca muere con ellos4
When the conjunction o is used to establish an equivalence, however, the adjective is inflected in singular and agrees in gender with the first noun:
El aerógrafo o pistola usado debe ser adecuado al compresor5
1: His hair and beard are tangled.
2: She showed up dressed in a white suit and mantille.
3: People of French origin and language are predominant in the province of Quebec.
4: Every time an elderly man or woman dies, a whole library dies with them.
5: The airbrush or spray gun used must be adequate to the compressor.