One of the much debated mysteries in H-1 NMR relaxation measurements of bitumen and heavy crude oils is the departure from expected theoretical trends at high viscosities, where traditional theories of H-1-H-1 dipole-dipole interactions predict an increase in T-1 with increasing viscosity. However, previous experiments on bitumen and heavy crude oils clearly show that T-1LM (i.e., log-mean of the T-1 distribution) becomes independent of viscosity at high viscosities; in other words, T-1LM versus viscosity approaches a plateau. We report 'H NMR data at ambient conditions on a set of pure polymers and polymer-heptane mixes spanning a wide range of viscosities (eta = 0.39 cP <-> 334 000 cP) and NMR frequencies (psi(0)/2 pi = f(0) = 2.3 MHz <-> 400 MHz) and find that at high viscosities (i.e., in the slow-motion regime) T-ILM plateaus to a value T-1LM> alpha omega(0) independent of viscosity, similar to bitumen. More specifically, on a frequency-normalized scale, we find that T-1LM> X 2.3/f(0) similar or equal to 3 ms (i.e., normalized relative to 2.3 MHz), in good agreement with bitumen and previously reported polymers. Our findings suggest that in the high-viscosity limit T-1LM, and T-2LM, for polymers, bitumen, and heavy crude oils can be explained by H-1-H-1 dipole-dipole interactions without the need to invoke surface paramagnetism. In light of this, we propose a new relaxation model to account for the viscosity and frequency dependences of T-1LM and T-2LM, solely based on H-1-H-1 dipole-dipole interactions. We also determine the surface relaxation components T-1S and T-2S of heptane in the polymer-heptane mixes, where the polymer acts as the "surface" for heptane. We report ratios up to T-1S/T-2S similar or equal to 4 and dispersion T-1S(w(0)) for heptane in the mix, similar to previously reported data for hydrocarbons confined in organic matter such as bitumen and kerogen. These findings imply that H-1-H-1 dipole-dipole interactions enhanced by nanopore confinement dominate T-1S and T-2S relaxation in saturated organic-rich shales.