You seem very determined, so here is more:

The easiest and most accurate way to compare two results: Put them exactly on top of each other and switch between. This lets your eye catch the subtle differences. I find it aids comparing, and learning too. (Does anyone know how to create an image file with layers in ImageMagick?)

There is filter talk at the GIMP or Photoshop forums. And entire college courses. But since results are so image and human perception dependent, it is all directed trial and error in the end. Since they are all just variations on resize (resampling), many filters will give very similar (even identical) results for a given image.

You haven't shown us a sample image, but I stand by simpler filters working best for cartoonish-colored drawings. The filters that make use of more distant neighbors are really intended for real-life colors as in photography.

If a point filter works best, check out -sample. I'm not sure what it is, but I also ran across -adaptive-resize.

More can significantly impact your resize than just the filter. You already hit on a post sharpening step. I recall that sharpening is most important for size reductions, but I'm not positive. Also consider gamma, colorspace, and color profile. These three concern the basic question of resampling: What exactly is halfway between two points, black (#000) and white (#fff) for example? More on this if anyone desires and already understands what gamma, colorspace, and color profile mean.

You mentioned an alpha channel. This could be separated from the image and resized using its own filter or sharpening. Unfortunately, I don't have and specific ideas here.

I don't claim to be an expert, so these were more ideas than advice.