How can electrons flow through superconductive material
I believe you should keep the following distinction in mind:
Ideal Conductors (temperature doesn't matter)
Ideal conductors have zero resistivity and hence infinite conductivity. But they are just idealized connection used in lumped models circuits. You can still treat the indeterminacy of the ratio j = E / sigma (the local form of Ohm's law) as a 0/0 kind of limit that gives a finite value for j.
Try to see this in this way, the resistivity of the 'ideal conductor' connection is so low, that you only need and infinitesimally small electric field in order to sustain the finite current through it.
So, you can still think of Ohm's law (as defined in lumped circuit theory) to hold, albeit in the limit.
Real Conductors (at low temperatures)
To successfully quantitatively explain conductivity in the real world you need quantum mechanics. The classical model of Drude (and even the semiclassical model of Sommerfeld) are not able to explain experimental data, especially at low temperatures (where low means in the single digit kelvins).
In the quantum theory of conductivity, the electron is seen as a wave (packet) interacting with the periodic potential of the atomic lattice of the material. It might surprise you, but if the lattice is perfectly periodic - that is it has no defects, impurities and it does not change its structure - this theory does not predict any resistivity for a real conductor. The electron will travel unimpeded in the material just like light would propagate unattenuated in a perfectly transparent crystal (the transparency is a consequence of the absence of impurities, defects or deformations).
What explains resistivity (and the exchange of energy between electron and the lattice) are imperfections in the lattice. They can be of two kinds: impurities and defects, and vibrations (that, in the quantum realm, are quantized in the form of phonons).
Now, by reducing T near zero kelvins, you can eliminate the vibrations and the associated electron-phonon interactions that lead to the resistivity you can experience at 'human' temperatures, but you cannot get rid of the impurities and defects in the materials. The result is that real conductors at very low temperatures will exhibit a residual resistivity rho_zero and you will not see superconducting behavior.

source: http://what-when-how.com/electronic-properties-of-materials/electrical-conduction-in-metals-and-alloys-electrical-properties-of-materials-part-2/
Copper is a metal that behaves this way.
As you can see, you will not see R-&gt;0 as T-&gt;0, so there is no paradox. You do not even need the passage to the limit adopted to explain ideal conductors.
Superconductors (below critical temperature)
Superconductors are a different story, and here the effect is doubly weird. Due to an exclusively quantum interaction between electrons, the resistivity of these materials actually drops to zero under a certain temperature. The way resistivity change with temperature is like this

source: https://www.ques10.com/p/31326/define-super-conductivity-and-critical-temperature/
but when you are in the 'superconducting state' you have already kissed goodbye to Ohm's law, so there is no point in my opinion to treat this case as if Ohm's law was still applicable.