It's one or the other. You can use the phase-change thermal compound that is included, or you can use paste, but not both.
Though many people have biases, if you are running a non-oc system, the phase-change thermal compound is perfectly acceptable. In my own unscientific tests, there was maybe 1-2deg C. difference between using the included thermal compound and using Arctic Silver II on a FOP32-1.
Edit: You are obviously going to have to remove the HSF because you put goop on with the gum. Now your choice has become significantly easier. You can only go with paste now.