Hi,
Not sure if I understood it right, so feel free to correct me if I'm wrong, but you seem to be interested in a cross-lagged panel model.
In this case, instead of creating a LGM to each variable, you should make a single model with both variables together and each variable at time t would be caused (regressed) by itself and the other variable at time t-1.
However, I understood you estimated a latent intercept and latent slopes of a non-linear function. In this case, I've never seen anyone correlating intercepts and slopes of two different models. Maybe you could plot the line described by these functions and compare them.
Best,
Yago