Since there are several rather strict requirements for sample surface (roughness, tilt) it may be very difficult to provide polymer specificity with such properties, especially taking in account that surface also should not be hardened by polishing.
the problem is that we are focused mostly on bulk properties not on coatings and already faced some problems with specimen preparation - gravimetrical casting does not desired quality of the surface.
No doubt that polishing could result in indentation size effect in your materials, however you should be able to polish your samples as long as you know how deep your indentation will go. You need to allow for the affected size when you are running your indentation test. Basically your indentation test should not be within this depth range.
See "Langitan and Lawn , J. App. Phys., 40, 10, 1969, 4009-4017" for the information they provide on the how the affected region size correlates with the nominal polishing grit size. This is just an example to understand this problem better.
I think ur results can be improved by following strict SOP for the sample preparation. One should use nano purified water and other acidic solvents should be accurately used for sample preparation regarding their molar solution conc. maximum papers dont tel the audiance that how they have prepared different conc of acids. Although this is basic but highly imp in your areas of work. plus I favour the comments of Janusz
Flat, scratch free and smooth surface are needed for nanoindentation. As, it can change the indentation depth, surface preparation will affect your determined properties. You can polish your sample using mechanical polishing. Try to start from lower grit of polishing powder. For every grit, after polishing check the sample surface using optical microscope. I used 200,400,600,800,1200 grit sequentially. Also remember, if you do initial grinding of your sample, make sure your grinded surface is horizontal. Other wise, it may affect the indentation.
You have to fix the sample, since it is very important not move it during the analysis. You also need a clean surface and then you need to choose the nanindentation parameters. As you stated the roughness can affect the measurements. Thus, you have to select an appropiate nanoindentation deep