2D meshing 1 metre thick
 

I am modelling a two-dimensional water wave tank with a Rigid Body floating object in the centre. The Domain is 75 metres high and 500 metres long with a wave maker paddle on the left and a beach on the right. A picture is attached.
I require a fine mesh close to the horizontal centre line that gets courser further away from the centreline. In the centre is a Rigid Body floating object that is to be surrounded by a fine mesh. The geometry is 1m thick and I only want the mesh 1 element thick. How should I go about this?
I am aiming for a 100mm x 100mm mesh around the rigid body, and along the horizontal centre line throughout the domain a mesh 100mm high and 400mm long, getting courser away from the centre line. The geometry is broken into pieces vertically to help with the meshing and horizontally to measure the wave height.
I have tried using a thinner model (up to 1mm) than 1m but have been advised to use a 1m thick model to prevent differences in y being close to the precision accuracy compared with differences in x.
How should I mesh this?