If the current is limited by resistance, nearly all of the energy is going into heat, not into accelerating your projectile. The way an inductor works, is you place a voltage across it, and the current builds at a rate that depends on the voltage and the inductance. The equation is:
dI/dt = V / L
In a coil gun, each coil is receives a short pulse of current and they are energized in series, with timing that keeps the pull just ahead of the projectile. The fact that the pulse is short can let us limit the current via inductance, rather than resistance.
Let's say the inductance of the coil is 1mH. Then if you put 1V across it, it, the current in it will rise by 1A for each millisecond the voltage is present. with 100V it will rise by 100A for each millisecond. Note that the diameter of the wire does not come into this equation (as long as it is big enough to carry the ultimate current) So you want to use very big wire to keep the resistance low and therefore the loss to heat low. Note also, that unlike the resitance case, the voltage does matter now.
Let's take your example of 125A. If the inductance is 1mH then we can apply 40V to it for 3.125 ms to get the current up to 125A. If we do this with wire that has very little Resistance , we can manage the heat by cutting off the voltage after this 3.125ms.
But even that is only a small part of the story of designing a good coil gun. The moving projectile becomes magnetic and is generating a voltage by moving through the coil. This is called back EMF. This subtracts from the voltage you are placing across to the coil, meaning you need a higher voltage to push the same current through.
This is what I mean by limiting the current via inductance and back EMF. If these are the dominant factors in limiting the current, rather than resistance, then you can transfer a much higher percentage of the power to the projectile and less to heat.
Ideally, the current would build up, limited by inductance until the projectile was in position to be accelerated. Then the back EMF would equal the applied voltage bringing the voltage to zero and all of the energy would be transferred to the projectile!
I don't know exactly what the ratio would be, but for an Ohm's law limited system, I am going to make a wild guess that you would giving no more than a few percent of the energy to the projectile.
Bob