How reasonable is it to assume that these particles are producible in principle?
Physics in our age progressed in steps. Starting from Rutherford scattering the experimentalist have explored scatterings at higher and higher energies with different targets and projectiles. The theoretical study of these data led to the Standard Model of particle physics. The steps leading to this picture we now have of elementary particles and their interactions were also for theory progressing slowly.
From the gauge theory of electromagnetism to the gauge theory of electroweak to the gauge theory of SU(3)xSU(3)xU(1) the steps were logical and esthetically satisfying. This has led to the search for a theory of everything including gravity, and string theories are the candidates for this.
The particles predicted by the electroweak unification were found experimentally. There are now a plethora of particles coming from tentative models with supersymmetry included ( which follows from proposed string theory phenomenology) and these new particles in principle could be detected at the higher scattering energies of the LHC.
Could there be a new conservation law that makes it impossible for ordinary matter / anti-matter collisions to ever produce these particles?
Not within the current theoretical models following string theory phenomenology. The conservation laws are known and are compatible with the creation of any of the particles given enough energy.
Would this conservation law contradict what we currently know about the Standard Model and laws of physics?
Could there be low to medium mass dark matter particles or superpartners that we'll simply never be able to produce?
If the masses are within the energy ranges of the LHC and the production cross section within the measurement possibilities we will see them. Otherwise we will get limits.
Or does the interaction with gravity ensure that these particles would always be producible, in principle?
Within the Standard Model the gravitational interaction has little to do with the production of particles, as it is orders of magnitude weaker than the other forces. If the masses are low the cross sections within the range of the LHC possibilities, they will be found ( and are sought for), as a missing mass signal, if nothing else.