I am, it should be made clear, assuming that the subject population is responding much like the average person in Europe did when their village moved from one kingdom to another - the nobles mostly left them alone, their taxes usually didn't change much, and they mostly carried on with their lives without much caring who was ultimately in charge. In the context of a sci-fi invasion, the real troupblemakers would be the former leaders and nobles.
This is mostly what i'm looking at. The common people by and large are fine with the conquest... alot of them see the advanced people as gods and pretty much welcome them in.
The former leaders and nobles by and large get to stay leaders and nobles if they're willing to play ball.
Exactly how many of these MP companies you need will depend on how dispersed the subject population is. Obviously, if the occupying force is being truly oppressive, you need more garrison troops. Against a truly hostile, actively resisting population, you could get as bad as needing one MP for every 10 locals, plus 2 more MPs so they all have a chance to sleep.
They wouldn't be particularly oppressive at all, and go with more of a "hearts and minds" approach. They'll move into a population center and immediately try to improve some aspect of their lives with some of their technology. They don't generally want to depose local leadership, just bring them into the fold.
They're a bit more Romanesque in their conquering. They just want to plant the flag, get some taxes, and call you a part of the Empire. Other than that, you can pretty much do what you were doing before.
In my situation here, I have about 35,000 people to work with for this invasion. The world could even be a bit less populated than 300 million but that seems like a good stand in number. Most of those 35,000 aren't soldiers, they're general civilians but they are loyal and willing to basically do what they are told.
Your numbers actually kind of work out to what my preliminary forces... there's about 1,000 soldiers who are both genetically enhanced (they're basically Trek Augments) and armed with various sci-fi weaponry (at least a portion of each company has some sort of power armor). I initially had them break off into 10 Companies of 100 to set about conquering the planet, with the pool of the 35,000ish civilians to conscript and utilize as necessary.
I think my general could actually work here, also assuming that at least SOME of the population centers will put up little to no fight and just surrender.