Which is the major product of bromination of 3-(dimethylamino)benzamide, ortho or para?
Here's the 3D structure of the substrate:

As you can see, the $\ce{-N(Me)2}$ group is clearly larger than the $\ce{-CONH2}$ group. Also notice that the $\ce{-N(Me)2}$ group is planar with the benzene ring. This is because this structure is the most favourable for $\mathrm{p-\pi}$ conjugation 1.
Your guess that A would not form is correct. The large size of the $\ce{-N(Me)2}$ group would also point to the fact that C is the major product. For a better explanation of the major product, we can take a look at the 3D structures of B and C:


You can clearly see that in B, the bromine atom pushes the dimethylamine group out of it's stable configuration, where it is coplanar with the benzene ring. This requires more energy and also produces an unstable product. Therefore, C is the major product in this reaction.
References:

Novikov, V. P., et al. “Molecular Structure and Conformation of N,N-Dimethylaniline by Gas-Phase Electron Diffraction and Quantum-Chemical Calculations.” Russian Journal of General Chemistry, vol. 74, no. 8,2004, pp. 1247–53. doi:10.1007/s11176-005-0146-9.