I'm trying to figure out how to utilize "sed" to remove the last instance of a certain string in a file. Not on every line, just the last line containing certain text.

Here's one way:

Enter these 2 command lines:

# set var lastline to line number of last instance of string.
lastline=`grep -n "target string" targetfile | tail -1 | cut -d':' -f1`

# use sed to delete that line, if a value for lastline was found.
[ "$lastline" != "" ] && sed -e $lastline,${lastline}d targetfile > targetfile.new || echo "string not found"

Note that sed cannot write its output to the input file name.
This could also be done on one line, but that would require reading the input file a total of 3 times instead of twice and doesn't allow you to check if the string was found before doing the sed:
sed -e `grep -n "target string" targetfile | tail -1 | cut -d':' -f1`,`grep -n "target string" targetfile | tail -1 \
| cut -d':' -f1`d targetfile > targetfile.new