No, not upset at all. I did not include a first-order drag term to represent viscous dissipation, since one simplifying approximation is to assume an inviscid environment. The first-order terms would definitely add exponential damping to the oscillating waveforms.
As far as cross-terms, I will see what the sloshing literature has for these.
I definitely agree that the monthly and multi-year behaviors coexist but the question is how best to isolate these behaviors and whether superposition properties actually hold.