You can make the non-diffracting panels larger by: splitting the body in SpaceClaim into diffracting and non-diffracting surfaces (i.e. on the XY plane), re-importing the geometry into Aqwa, adding a Mesh Sizing control to the Mesh, and scoping this to the non-diffracting surfaces.
However... the non-diffracting elements do not add to the computational cost of the diffraction analysis, and increasing their size may reduce the accuracy of stability/time domain Hydrodynamic Response analyses, so I wound not recommend this unless you are exceeding the solver limit on the total number of panels. For your simple cylindrical structure I would not expect you to need lots of elements to get an accurate solution.
To check the proportion of elements that are failing the mesh quality checks: once you have turned on 'Ignore Modelling Rule Violations', when you run the diffraction analysis, the Aqwa solver will output a message like:
14 MODELLING RULE #1 VIOLATIONS IGNORED BY GOON OPTION.
This number (e.g. 14) should be compared to the number of External Surface Diffracting Elements which is shown in the Mesh details.