The flattened quilt has many small fluctuations such as:

These features cannot be extended without the edges running into each other creating a conflict. Changing the part accuracy will not help.
My suggestion is to created a new flat surface using the Fill command.

Use lines arcs and splines to sketch the new shape over the original, eliminating and smoothing out the variations in the edge of the flattened quilt. You may need to play with any splines (too many points will make it harder to get smooth enough) created to get them to work with a 3 mm extension. Also any arcs created must be greater than 3 mm to work. This is the only way I know of to extend your surface as the existing surface edges are too "dirty".
Below is an example of using arcs (construction features) fitted to one of the smaller features and the extension that would result.
