Given the two fitting intervals, a low range from 1880 to 1950 and a high range 1950 to 2016, we can compare the resultant parameters.
The strongest lunar parameters are the D=Draconic and A=Anomalistic periods. The higher-order parameters $D^n$ and $A^n$ also align as does a cross-term $D\cdot A^2$. The $D\cdot A$ cross-term is negligible.
One thing you will notice is that the overall amplitude is different on the two axis. That has to do with the error metric used - optimizing WRT a correlation coefficient does not preserve the absolute scale. It does take a few minutes to do the optimizing fit on each range but the resultant alignment is correlated above 0.99.