Idea 1: Use a special algorithm to double the image size
Standard resizing algorithms don't add more detail. There are some algorithms designed for that (Scale2x, 2xBR, etc.) but they don't work well on anti-aliased images, due to the pixels with intermediate colors.
However, there is also Waifu2x, which is a machine learning algorithm that works well on anti-aliased images. Here is the 2880x1440 result of this (make sure to convert to .tif if you want to use it in Geocart):
It's pretty nice. Here's a comparison of 1440x720 version, scaled 2880x1440 version and Google Maps on Poland:
Unfortunately, it cannot be scaled 2x again, because of the 1500x1500 limit.
