I think I will respond to my own initial post as I think I have found the best procedure regarding the BCC Stabilizer and transitions in FCE; I tried both the other suggestions but with longer clips, it was a time consuming process so I finally tried what I should have done first; trimming the clips, add the transitions and then in the end, add the stabilizer where need be, either to stabilize or to smooth. That way it works. What I did wrong, was to add the stabilizer first.
Well, just in case others fumble as much as I do:)