In case of gravitons, there is no a hypothesis of quantization in conjunction with some sort of a black body radiation and something like a photoelectric effect, so the quantization of gravitational waves stays a hypothesis.
Any quantized energy level gets a width $\gamma$ (or a shift) if some additional interaction is included. For independent interaction mechanisms the corresponding gammas are added:$\gamma=\sum_i \gamma_i$. Emmiting a graviton is highly improbable, so an excited state of a neutron $\psi_n$ in the experiments above decays or gets excited even more due to other, much more probable interaction mechanisms.
P.S. Maybe I was not clear in my answer. Let's recognize that not everything must be quantized. Huge ocean waves must not be quantized - their classical description is sufficient for our purposes. If you still like quantization approach to them, consider the practical case when we are bound to deal with always coherent states of high amplitudes, and when a single quantum of an ocean wave may not be observed - under no circumstances.