Thanks for all of the responses!

So:

Consider Altis Belem or Fontecruz Lisboa in Lisbon instead of Sheraton or Marriott: Will do. We were thinking of using up some points and the Fontecruz did not offer a rewards points rate, but Altis Belem did, and I will double check to see if Fontecruz opened up.
Stop on the way up to Porto to see and enjoy Nazaré, Batalha, Óbidos, Coimbra, and Aveiro. Consider cutting one night from Lisbon or Porto to stay at the Bussaco hotel: Wow! These all look stunning and charming! Can I get to Bussaco by rail?
Take a day trip to Evora from Lisbon: We can do that. The historic sites look exactly our style.
Drop the AC Porto: Done.
Look into pousadas (which sound absolutely intriguing): we absolutely will. We had never known about these before but they sound exactly like something we would love.

Has anyone stayed at the Intercontinental in Porto?

These are very helpful! Thank you! The help of the FlyerTalk community enhances our travel in so many ways.