"Second thing, the problem on Earth is coolant. In space, you have the ultimate coolant - absolute-zero hard vacuum."
There's a major problem with that statement.
You can classically cool things in three ways. Convection, conduction and radiation (there are some more esoteric ways, but these are the practical, engineering ones). Of those, both convection and conduction require physical contact with matter - in fact convection requires conduction, it's just that the process moves the coolant fluid, which can also be done by pumping and so on.
In space, that leaves you with radiation alone - basically black body radiation which, for a given temperature, emits energy at a fixed rate. That's it - the only form of cooling you have. It matters not a jot that the virtually empty space around you is at near absolute zero - if the few particles in space were at 1,000K it would make no difference to the rate of cooling (well there is an integration to infinity thing, but leave that out for the moment).
One of the problems of space travel is cooling high output systems (chemical rockets get round it by chucking the hot test stuff out the back). The only two ways you can increase cooling capability is by increasing the surface area or running at a hotter temperature. The power dissipated goes to the 4th power of temperature, so there is a very steep curve. A metre square metal plate glowing to red-heat will radiate quite a lot of energy, but if you start trying to run reactors generating 10s of megawatts then that's going to require a large surface area. If you need to cool things down to the temperature required for semi-conductors then that area will increase disproportionately due to that 4th power law.
Cooling a nuclear powered rocket is a serious engineering challenge, not least because space is a vacuum. The numbers can probably be made to work, but the termperature of a near vacuum is absolutely no help at all.