How far is it to Pluto?

I'm a screenwriter and I'm currently writing a sci-fi short about a journey from Earth to Pluto.

The title of the script is "Three Billion Miles To Pluto" and i wanted to know if that was accurate. I've read that, at it's closest, it's around 2 billion miles from Earth...so I guessed that at some point in its orbit, it would be 3 billion.

But there's another factor...in the script, the ship (called "The Hades") makes a brief stopover at a research station in orbit above Mars, so I'm wondering if anyone could tell me if a journey from Earth (actually, the moon) to Mars to Pluto could still take place within a distance of 3 billion miles.

Thanks for the help...it's a small thing that the audience wouldn't notice, but I'd like to be as accurate as possible.

Pluto's orbit is inclined quite a bit from the orbits of the planets. Also it's more elliptical. That may be one of the reasons why it really is not a planet. Maybe it got captured somehow or it got perturbed a lot. It's awfully small. Its distance from the Sun (and the Earth) varies quite a bit, perhaps +- 25 percent. A couple decades ago it actually got inside the orbit of Neptune. Now Pluto's getting farther away and dimmer.
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I don't have an exact year for the story though it's certainly no sooner than 50 years from now given that there is a launch site on Earth's moon and an orbital space station above Mars, and possibly a colony on the planet itself.

In terms of the technology, well the ship makes the journey in 10 months, so the ship is pretty fast and the crew spend most of their time in stasis.

The ship's engine is an "Ion Drive" but don't ask me how it works because I pretty much went with standard sci-fi where an Ion Drive is standard.

I kept the exact year vague for the purposes of the story, but I would say between 100 and 200 years from now.

Lousy acceleration but economical for long hauls. If you land it on anything with significant gravity, it’ll never take off again without boosters. It would probably need auxiliary thrusters for getting in & out of orbit and other such manoeuvres. Unless ion-drive technology vastly improves beyond what is currently envisioned, of course.

A little over a hundred years from now Pluto will be at aphelion, which means that it will approach us again over the following century. I figure the distance will become less than 3,500,000,000 mi. (making your title apt, taken to the nearest billion miles) sometime around 2190, remaining ‘within range’ for the next eighty years or so.