why not just create a plane that has a matching aspect ratio? You've already figured out that Maya stretches or squishes the texture to fill the entire surface area.

As for the attribute editor; using a coverage of less than 1 in U or V will reduce the covered ared. More than 1 will essentially crop some of the texture that exceeds the surface area. However, it will be difficult to get the aspect ration exact in the AE.

The other fix, you also, already figured out, is to map it and apply the texture only to the areas the UVs cover, hence your loss of resolution. On resolution, as long as you're not doing the model for a game, or some other purpose that places limits on texture map size then you can use a larger map size. Just be aware that your file size will increase accordingly.

Good luck