Let's talk about fence posts
Have you ever driven a fence post into the ground? You betcha! You get one of those cool tubes with handles and bang! pound that sucker right in.
Now, I want you to keep that in mind as we talk about magnets. (Heh, you're going to love this. Trust me.)
A big-ol' magnet is resting against a block of iron. The magnet is the Earth and you want to separate the iron (your rocket) from the magnet. The pulling force of your arm is similar to the pushing force of the rocket exhaust. Why is this important?
Because you said your FTL drive creates negative mass!
Not much, but it's there!
You have that magnet and block of iron far enough apart that, at rest, the magnet doesn't pull on the iron (ship in orbit), but you just changed that block of iron into another magnet with the opposite pole pointing toward Earth!
Bang!
Your fence post (space ship) was just pounded a couple of feet (with an appropriate crater) into the ground.
Yeah... fence posts...
No one in their right mind would activate a negative-mass-inducing engine within the gravity well of a planet. You might have trouble activating it within the orbit of Mercury. Bang! It might cause a cool solar flare.
BTW, I recognize that I'm treating negative mass like the opposite pole of a magnet. Technically, two positive masses attract and two negative masses would attract. Opposing masses should repel (the opposite of a magnet). That's not as cool as my fence post metaphor, but it's worth noting. The repulsion would cost your your navigation completely. It's the same bang! but it's more like a bullet from a rifleblunderbuss than two magnets.
But I wasn't willing to walk away from my fence post metaphor. Sorry.