I would suggest an old trope, "hyperspace" or "subspace" as the venue for the actual travel at FTL. This is used in modern shows like "Dark Matter", their FTL is not in any kind of real space; so there is no kinetic energy in the real space. When they "drop out" of FTL, they are at a standstill.
This inability to hit anything at FTL is pretty much a necessity anyway; otherwise you could hit stars, planets, asteroids, dust clouds, even gas clouds would have pretty much devastating impact force (incalculable, really, since we don't know how to account for relativistic effects at all).
Stop thinking of FTL as operating in our current 3D space, and think of it more like wormhole tech that takes a ship to another plane or "dimension" that is a million times smaller than our space, and moves it slightly there: to the crew a 20 mph move for an hour is a light year. So your multiplication factor (or in Star Trek, the "warp" factor) is 293 billion x light speed. Call that a 'warp factor' of 2.93. But when the ship leaves that dimension, it is just traveling at 20 mph, a virtual standstill. On the straight line from where it began to where it ended, it makes no difference if it "traveled" through a star or supernova; it wasn't really in the universe at all.
Inside that dimension, we have only figured out how to travel in the under 100 mph range; so warp factors up to about 15; but they require exponentially more energy, so if it isn't an emergency, they don't exceed warp factor 3.
For more restrictions; limit the size of the field that can be formed to put something into this other dimension: We can't move anything larger than X at FTL, the bubble isn't big enough. So maybe a spherical ship a hundred yards in diameter, but nothing larger.
You can also limit the mass of anything in that bubble; perhaps nothing more than that amount of water. (for a sphere of radius 150 feet, and water weighs 62.43 lbs per cubic foot, about 883 million pounds; or 441,292 tons).
And you can limit the maneuverability: At FTL you cannot maneuver at all, you travel in a straight line until you punch the button to drop out. In fact, for your story purpose, you can require the field to be practically standing still relative to any major gravitational field in its vicinity; be it planets, moons, or a star; if the ship is moving then the gravity gradient is changing, and that prevents the FTL bubble from forming; and the reverse is true upon exiting hyperspace: Say you have to reverse the polarity of your FTL bubble, and that is impossible to do if the gravity gradient is changing too rapidly. It is impossible to enter hyperspace at a high rate of speed, and impossible to exit hyperspace and be traveling at a high rate of speed.