Modelling sea levels with gravitational parameters
Starting from scratch and building a "toy model" is unlikely to be successful here, because while you could certainly model Newtonian tides, much of what happens on the continental shelves is tied very closely into the shapes of coastlines and bathymetry, the interaction between the inertia of the tidal wave and friction on the seabed, and so forth - a lot of non-linear effects, some of which are not fully understood.

My suggestion would be to start with an existing, validated, global ocean model and tweak its input parameters. For example, to simulate a change in the gravitational pull of the moon you could change the amplitudes of the lunar tidal constituents that drive the model (and perhaps also their periods, if you wanted to work out the appropriate orbital mechanics!).

Be aware that running models of this sort tends to be computationally expensive, obviously depending on the resolution - but it should be within the realms of what is feasible on a home computer, if you don't mind things taking a week or two to run (I assume, since this is a hobby project, that you don't have access to HPC resources for it). I'm not sure whether anybody makes a simple but validated model openly available - if anybody knows of one, perhaps they could comment. If not, you might have to build your own using an open source code, which would be substantially more work.