You are correct that there were certainly strands in Roman philosophy that tended towards what we may call "pantheism" as opposed to polytheism. I think it is a bit of a leap to go from accepting the Stoic idea of natura to rejecting the traditional pantheon (one might view Jupiter, Minerva, etc as aspects of natura or divine beings "below" natura) but I would agree that there were certainly those who made that leap. That being said, this was not representative of all Romans, or even representative of the upper classes. People continued to erect monuments and do homage to the traditional gods.

In some ways, it may be easier to consider how monotheistic medieval Europe was. It had a Trinity, which in theory was one God - but with three manifestations. It also had Mary, who was in practice nearly a goddess (and a very accessible one at that!). It had a large array of saints, to whom prayers were made by people who often saw a local saint as more approachable than a remote deity. Then there were angels. And of course the folk retained beliefs in an array of supernatural beings in the forest and the field, who had nothing to do with Christianity, but which persisted as powerful entities who demanded appeasement and could affect lives. So one could argue that medieval religion was more henotheistic than monotheistic.

We can project backwards - with a great deal of caution - to imagine the belief systems of the Roman world. We must say "systems" in the plural because the Roman world spanned centuries, a great deal of geography, and a full range of economic classes with diverse degrees of education. So there are no singular answers to your question.

That said, we may regard some of the attention to "the gods" as being as much cultural and societal obligation as matters of maintenance of supernatural forces. Some certainly believed more than others when looking at the broad swath of time and place. At the same time, there clearly was - as there was after Christianization of the Roman world - an idea of a remote all-powerful force. This entity fascinated some more than others, but more importantly, the more omnipotent and omniscient the entity, the more likely people were/are to perceive that force as impersonal and removed from day-to-day events. There is a supernatural balancing act, consequently, which one finds in many cultures: as the "one" god gains stature, the lesser forces are the ones to whom one appeals for immediate action. We see that in the European peasantry shortly before industrialization, we see that in the medieval world, and so certainly we should not be surprised to see it before conversion in the Classical world.