Currently the heat transfer area in the reactor is the surface area of the inside of the reactor casing. This causes a problem because the heat cannot be transferred to the coolant faster then its generated. This leads to having a gigantic reactor casing housing a fairly small core (with the fuel rods).

For example a core that could fit into a 7x7x4 reactor casing needs a 13x13x4 casing for good cooling.

It would be nice to have blocks (fins or something) that you could add to the inside of the reactor which would increase the available heat transfer area. The Block could also increase the amount of coolant storage a reactor has.

I don't know how much realism that is being attempted here but from what I know about nuclear reactors there is a lot here that is pretty good. The passive reactor is by itself is highly inaccurate since a nuclear reactor doesn't generate electricity it only generates heat. Therefore using a turbine is the only real way to generate electricity. In that respect heat generation is much more realistic.
The surface area of the core doesn't matter but the rate of coolant flowing through the core (how much steam you use vs the amount it can generate) determines heat in the core. At that point the static fluid in the vessel (or solid material) in a real reactor is shielding and moderator. And that by and large takes up much more space than the actual fuel itself.
In the case of an 'active' reactor it serves the purpose of moderation to gain more efficiency from your fuel. I don't think that anything should honestly change to accommodate the desire for smaller designs since, if we are going for realism, wouldn't physically make sense.