I removed mine about 2 weeks ago. It's a '05 Edge with the 3.0. I did the same thing, rented the tools and didn't work! so I bought a strap, put it on and it slipped. So I figured it was dirty and it was! I cleaned the pulley real good & strap wrench and tried again. Mine is removed clockwise. yeah, go figure! I had my wrench to hold onto the engine fan; however, the wrench barely cleared the fan's blades so I couldn't get a good grip. I grabbed my rubber mallet, hit it several times really hard while holding tight onto strap wrench and it just like that it got loose.
good luck.