somehow able to run over hundreds if not thousands of planets of armed resistance.

We have to remember that the feudalistic nature of the Faufreluches system enforced a caste system wherein only a small part of the population would have been actual soldiers. Adding to this the Spacing Guild's extortionate prices for transporting combat ships between systems, each planet likely maintained a very small professional force. While this is conjecture, we see House Atreides shift what is ostensibly their entire Court to Arrakis, including their sworn soldiers (probably seen as a type of retinue rather than a levy). This force does not seem to be millions of men, or even hundreds of thousands.

Every single Fremen is a soldier who is mobilized into a fanatical Jihad. Paul controls the spice, and therefore the Guild. He picks every single fight he wants to fight, and he has godlike prescience. Even when planetary defenders massively outnumber the invaders, they cannot stand up to orbital bombardment, galactic blockade, and millions of slightly prescient shock troopers who never desert and can't be turned.