No, I'm not [applying conservation of momentum], I'm simply assuming that the drive is pushing on something. By definition, Power = Force * Velocity.
What?

I have a definition power P = iv, so that means the 500T ship must have a net charge, and there must be an electric potential which accelerates the ship.
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Well, since one volt is the electric field that will apply one newton of force to a one coloumb charge, these two definitions are in fact the same.
One watt = 1 joule/sec
1 joule = 1 kilogram m^2/s^2 = 1 newton x 1 meter.
See? Throwing out an equation is subject to conditions, and conservation of momentum is the condition of P = F·V just as Ohm's law etc is the condition of P = iv.
Actually, P = F*V is not dependent on conservation of momentum, it works just fine if you're pushing on an immovable object.
I used a one second average delta-vee to calculate change in KE instead of trying to figure out an instantaneous change of velocity equation
Here, I'll do it. This is first year calculus.
V = at +v0, where v0 is initial velocity.
F = ma
ke = 1/2 mv^2
= 1/2m(at+v0)^2
= 1/2m(a^2t^2 + 2 atv0 + v0^2)
power = d(ke)/dt
= 1/2m(2 a^2t + 2av0 + 0)
= 1/2ma(2at + 2v0)
= ma (at + v0)
= F * V
for a proper calculus integral for delta-KE.
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Derivative, not integral.
By my example grav drive was only 30% efficient at producing acceleration from input power (assumed electrical), which is hardly a "perpetual motion machine"
Ok, you have a device that produces 5 million newtons of force, with a power input of 250 megawatts.
Put it on a rotating arm, which we will assume the tip rotates at 100 meters per second. To keep it from going faster, we will attach an electric motor to the axle.
Now, we have 5 million newtons force * 100 meters per second, and therefore the electric motor, assuming 100% efficiency (which it will come close to) will output 500 megawatts. Of which 250 megawatts are required to power the gravity drive, and the remaining 250 megawatts may be used as desired.