Integers will improve your range somewhat, but not that much. If you set 2^16 to be a meter, then you still can't go past 65km. And as a downside now you have to be extra careful your derived numbers don't go out of range.
That's 64 bit. If you were using 64 bit floats you didn't have problems in the first place.
Also a granularity of 1mm will make slow movement complicated to calculate correctly. Consider updating at 60Hz and having an object that moves 1 inch per second.
