In short, tenses which were indicated by inflectional endings in CL were often indicated periphrastically

Yes. The development of the Romance future from past participle plus habere took place in more than Portuguese. Whether this was a late Vulgar Latin phenomenon or an early Proto-Romance one is hard to tell, as texts are scanty. I seem to remember Varo or Priscian talking about periphrastic constructions, but I may be wrong. You see the same thing in many present European dialects: the replacement of the inflected preterite with a periphrastic perfect. 'I sang' versus 'I have sung' kind of thing. The inflected versions tend to be more irregular.