Electrical – Gerber Viewer With Good Measurement / Distance Tools

In Eagle, the copper "polygons" are made up of many parallel overlapping traces. If the polygon's linewidth is set to something small, like 1 mil, it quickly consumes large amounts of data when converted to Gerber.

If you change the polygon's linewidth to something thicker, it will solve this problem. However, it also affects any thermals tied to the polygon, and can cause the polygon's borders to change.

If you need your current polygon settings, then I would suggest that you make a small-width, detailed polygon where it is important, and make a larger, coarse one over the rest of that layer.

Since image processing using GIMP is an option for you, I am posting this as an answer.

From the comments:

PNG format is capable of non-rectangular graphics (i.e., for example a circular image with a transparent/non-existent background)

This is not exactly true. PNG supports only rectangular graphics. There is no non-existing background concept. PNG uses alpha-transparency, which essentially allows to set the transparency for each pixel.

"flooding/subtracting the surroundings programmatically would be OK for me, except how would I choose exactly that area?"

Using GIMP, its easy to get this result in a matter of seconds.

1. To select the area around the PCB border you want to make transparent, I used the Magic Wand / Fuzzy selection tool. Go to "Tools" > "Selection Tools" > "Fuzzy Selection" (keyboard shortcut "U"). Then click on the respective area. Use the "Threshold" setting to set the range of color variations that are included in the selection.

2. In the Layer window, select Layer - Transparency - Add Alpha Channel. If this is blanked out then your image is already set to store transparency data.

3. Select Edit - Clear. This makes the previous selection transparent.

4. When you save the file, make sure `Save colour values from transparent pixels' is selected.