Well the size is unworkable for a practical ground design. We could try something aquatic, which might help with cooling issues, but there is still the power issue. If the cooling were not a problem, however, perhaps power would not be so limited and we could just use conventional I.T.C. power systems...
Meh, imma throw up the proposal anyways...
Stand-off Nautical
The S.O.N. is a Standoff that cannot fire in space, the cooling systems don't function there and the ship would be lucky to fire before melting. It has just enough fuel to reach a world and manage reentry. It comes packaged with disposeable heat-shields to survive a rough atmospheric entry and has multiple hollow compartments to facilitate floating.
once it lands on an oceanic body, it then engages water-cooling systems from oceanic water and a conventional power-system in the spare space that slowly recharges capacitors and runs energy-efficient propellors.
I don't really think that this is the best idea. It all looks revisiony to me, but it is a lot of things to expect from a revision, but it is an option and if we could just dump one of these on C2 to pretty much own the planet for the foreseeable future...
Stabilised HyMet
We refine the process to increase the purity of the material and enhance its structural consistency and enforcing optimum polarisation. The result of this technobabble is that it gets closer to, or even attains, being stable with no cooling systems.
Added: Assuming this is successful, we should like to add additional fuel with which to manoeuvre and withdraw after our single shot.
Size is killing us on the HyMet, I would like to get this sorted before working too much with it. It could open up ground-based laser vehicles and such...
Stand-off: Great
The S.O.G. is just an enlarged chassis with the same-sized laser. All the support components have been enlarged or increased to allow repeat firings.
Ought to fix most of what is wrong. I am kinf of more worried about the detection facilities though. Shooting first is a big deal...
Also it is interesting to note that lasers are a short-ranged option here. We could later build laser drones to go into medium range away from the support vessel. Or research beam-confinement. Or run missiles alongside lasers... There are options, but for now lasers are going to diffuse in a vacuum...