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I am writing a scifi novel based roughly four hundred years from now, and it occurred to me that the planets and other objects might not be quite where I need them to be for certain travel details to make sense.

Primarily, Eris and Pluto have irregular orbits that take a very long time (558 and 248 year respectively), which sometimes puts Eris closer than Pluto. This is a problem if I write that Eris is the last stop before exiting the solar system if Eris is at ~38 AU (perihelion) and Pluto is at ~49 AU (aphelion).

Are there any software tools available to accurately map the solar system hundreds of years from now?

JPL's HORIZONS system will give you ephemerides, charts of a planet's location in the sky (via right ascension and declination) and position in space via quantities like the true anomaly. You can find ephemerides for all eight planets, as well as about 800,000 asteroids, comets and moons (yes, including Pluto and Eris).

HORIZONS is quite accurate, and allows you to make calculations in a variety of timesteps (and shows you intermediate positions along the way!), ranging from days to years. The shorter the timestep, the better the accuracy, but the longer it takes. Usually, it can calculate ephemerides for up to 500 years in the future.

There are a number of interfaces, with the simplest being the web one. Pick the option that suits you best.

Starry Night is pretty reliable.

The Universe Sandbox has the ability to simulate planetary physics. I doubt that it is 100% accurate, but as a tool for projecting a future it may fill your need.

Alternately, the math for working out roughly where a planet is in its orbit is not overly complicated. Find when their next perihelion/aphelion will occur, and simply add the time required to complete 1 orbit. Another nice thing about perihelion/aphelion is that the planet takes about half the orbit time to go from one to the other.