Depends if you go up/down (It's like a fried egg) or out to edge. The galaxy is oval too, so I forget which axis 100,000LY is. 13,000 LY sounds too much for up/down and too little for nearest in plane of galaxy, I'd have thought more like 20,000 LY, but I always have to look stuff up for exact figures so could be wrong.
New Horizons is very much faster. Voyager has no propulsion. A decent continuous propulsion system will take you far past Voyager in much less than six months.
But six months of 1G is about the practical limit even for Fusion power unless you refuel. So without a Jump/Hyper drive or Star gate/portal / wormhole you need to use less than half the fuel and then coast till a suitable distance away from destination, point thrust at destination and accelerate at same amount as before for same time, roughly. Hence you need a margin of fuel for final navigation and orbiting.
If your craft has a Jump engine that only works in deep space (say just outside Knuipner belt and WELL inside Oort cloud), then it turns out the best strategy for fuel is to NEVER orbit, you drop "shuttles" and "shuttles"/"rockets" already on a planet rendezvous as you "whizz" past. The extra fuel /mass and energy (even if fusion) to break from a deep space jump (as you'll still have the velocity you reached accelerating to deep space) to actually orbit is very much more. The 2nd lot of craft already on the planet re-supply and refuel the passing Starship and are taken on board to be "dropped off" at the next Homeworld transit (where you pick up a new lot). As jumps can be a different direction to the normal space velocity, the Starship can go back and forth between two Homeworlds repeating the same manoeuvre adjusted gradually due to planet's orbit.