that is 300dpi is not written or even part of the image format.
You will need to specify the intended DPI resolution (using -density) before reading to get the desired final size.
NOTE within EPS is a string, something like
This specifys the image bounds (though it could draw outside these bounds) that the contents are located. They are in 'points' (1/72 points per inch) and as such are dependant on the 'density' (pixels per inch) the image is read in at.%%BoundingBox: llx lly urx ury
IM should handle that conversion (via Ghostscript) perfectly fine.