Ha - I spent two weeks leaving from St. Vincent and still didn't get to do all I wanted! There is never enough time!
I know that a few people on here have done St. Lucia one way to Grenada in about a week, but not sure how they made out.
I also think that spending time in St. Lucia instead of trekking to the Grenadines is a better use of time unless you can arrange a one way.