OK -- so I've figured out what causes the gridlines, but I don't know how to solve it. If I import graphics into a tileset with the settings "Scale (Highest 4x)" and either "bicubic" or "bilinear" resizing, I get the permanent gridlines. If, instead, I import the graphics using either "no smoothing" or "2x scale" (w/ the bicubic/bilinear smoothing on), there are no gridlines ... (but the graphics look bad without the smoothing or at the wrong scale.)
I will certainly still pass along a sample game if you think that would still be helpful. How do I do that? (I have some programming experience in Blitz Plus, but I'm very new to Stencyl).
On a side note -- how common is it for a Stencyl game to include all hi-res 4x scale graphics? Does the game size get out of hand very quickly? Should I maybe be aiming for mostly 2x scale and save the 4x scale for select things?