Unfortunately, there is no way to do this.
The map must have a side size of a multiple of 256.

In your case, you need to use the texture 768x1536 + Sprite Mask.
https://docs.unity3d.com/Manual/class-SpriteMask.html

The map itself is just set to a fixed GPS and zoom level, with no interactivity. It's just there as an image. I am using a Sprite Renderer map, since that appears to be the most simplest type of map there is.

However I cannot resize the map to the size of the parent panel. It renders to the 512 x 512 texture size, but I need it to be 693 x 1291 pixels.

How can I resize the map to this size?
Or should I try to "oversize" the map sprite render and use a mask to trim it down to the required size?
What is my best option?