The problem is that Portuguese identity sort of developed in explicit opposition to Castillan/Spanish culture. This was the case from the very beginning. As far as I know, galician was the language of the Leonese court at the time of Portuguese independance. So, independance did not really happen so much because of pre-existing cultural differences, but more because Portuguese nobles felt that they were being neglected by the crown. Portuguese culture pretty much started there, at the time of idependence, with our founding mythos, the war agaisnt the Leonese crown being an important part of it. So, in a way, the word "Portuguese" at first meant simply "Not Leonese", and later "Not Castillan" and "Not Spanish". It's true that, for a time, the word Spain meant simply the Iberian peninsula, and, in that sense, the Portuguese called themselves Spanish, but doesn't mean that they felt part of a larger Spanish polity. It's very hard to get Portuguese people to believe that they can be Portuguese and Spanish at the same time simply because a huge part of Portuguese identity was built in opposition to the remaining Iberian nations.
Now, that said, I don't believe we necessarily need to have a PoD that goes back to the medieval ages in order to get a unified iberian peninsula. All we need is an alternate Iberian Union that consistently manages to secure the interests of Portuguese elites. Economic advantages will always speak louder than cultural and identity issues. If the Portuguese economy keeps doing fine for a while under a union with Spain, then I can see Portugual becoming progressively more integrated into a larger iberian polity. But in order to get that the Spanish are going to have to spend less money on Europeans wars and more on protecting Portuguese overseas possessions and trade ventures, and I'm not sure if you can have that with an Habsburg monarchy...