I'm not sure how you got those calculations. One of the shuttles on Voyager has enough firepower in the warp core to make an explosion three times the size I mentioned. Unless there is a huge exageration on the firepower of antimatter in Star-Trek Voyager, all I need to do is make an antimatter reserve in the missile that has a mass only one third the size of that warp core.
Star-Trek is physically non-sense - the energy output of a warp core is never the same between two episodes of the same series. If you want to play Star Trek, the reference to Bridge Commander already happened in the thread.
Also, how do you want to define destruction in your model? Lets say you assume a fictional material called handwavium, which makes up the hull of your enemies ships. This has thermodynamic properties, which are beyond what we have today. Now you calculate, how much radiation you would have to produce, so enough energy arrives at the enemy ship to destroy it.
To give you an idea about the dimensions: Titanium has a melting enthalpy of 400 J/g. This means, for melting one Gram of Titanium, you need an energy of 400J. Ideally in a short burst, so you don't loose energy by radiation from the heated target.
Melting a spacecraft weighting 750,000 tons and being made only of Titanium would take 750,000,000,000 g * 400 J/g = 300,000,000,000,000 J or 300 TJ (Terajoule) energy.
Now, lets assume your explosion energy follows the inverse square law (as you stated the destruction region is spherical). We assume a fireball radius of 25 km as source of the radiation, for making my math simpler (I did not calculate this radius, but do it better).
25,000,000 km away from the explosion center, the energy is 300 TJ. 25 km away, or one million times closer, the energy in the same solid angle needs to be one million squared higher: 1 Trillion times higher (12 zeros more).
Instead of 300 TJ, you will get 300 YJ (300 Yottajoule, a bit less than the energy produced by our sun every second) - and that in each small surface area of the fireball. If your target ship was 1 km large, this means a solid angle of 1/25,000,000 ~ 4.000E-08 radians. The surface area of a full sphere is 4 * Pi * radius^2, about 100 million times higher.
So, the full energy of your antimatter/matter warhead is 300 YJ * 4*Pi/4.000E-8 or 9.425E+34 Joule. Now, we can use the mass energy equivalence (Einsteins E=mc²) to calculate the minimum mass of the warhead:
m = 1.049D+18 kg.
If you think, this is now peanuts:
Our moon is only 7.3477D+22 kg. 70,000 warheads would weight as much as the moon. And this is a minimum mass.
You release as much energy in one explosion, as our sun in 11 years!
Do you now see why people don't like what you are want? Not only that you want brute force - getting your rocket from Earth to moon would already require the mass equivalent of a small natural satellite.
It is so unlogical, that only the disciples of Roddenberry could like it.