The last model forcing to arcsin comparison had low resolution. This is with a shorter Gabor window in the wavelet. The y-axis scaling is in octaves (each unit is a period doubling based on the fundamental unit, in months or days)
Here you can see the stationary periodic components more clearly and how the detail matches. The third chart changes the resolution from monthly to daily. The fourth removes the annual impulse multiplier which essentially unaliases the signal, showing the underlying monthly and fortnightly tidal signals (the top 2 lines). Those can be compared to the tidal signals in the differential LOD signal in the earth's rotation, which is the chart to the far right taken from the following paper:
B. F. Chao, W. Chung, Z. Shih, and Y. Hsieh, “Earth’s rotation variations: a wavelet analysis,” Terra Nova, vol. 26, no. 4, pp. 260–264, 2014.