You should not be afraid what set -x shows you. It just indicates where word boundaries and white spaces are found in it's own way but that is no what your command will be when called.
Nevertheless you should consider writing your expressions a bit simpler for the clear picture. For example:
TIMESTAMP=`printf '2015:12:29 %02d:%02d:%02d' $HOUR $MIN $SEC` EXOPTION="-overwrite_original_in_place -DateTimeOriginal=\"$TIMESTAMP\""