Thanks a lot for taking your time to go down so deeply into this issue! Changing the DPI setting to 72 for the splash image actually fixed the problem. I wasn't even aware that bitmap images can have (and need) such a setting in their metadata. I've also used this occasion to switch from BMP to a more modern PNG format for the splash image, since this is what Eclipse did a few years ago. However there too the DPI needs to be set to 72.
I've used the following command to change the DPI for an existing PNG image to 72:
exiftool -overwrite_original_in_place -PixelsPerUnitX=2835
-PixelsPerUnitY=2835 splash.png
The 2835 value is calculated as: round(72 * 1000 / 25.4) where 72 is the desired DPI. Perhaps this can be useful to others who'll stumble on this post.
I wish you a Happy New Year!