Hi,
Thank you very much to everyone who replied.
I ended up using a combination of measures to remove the tie rod end.
I bought a small 3lb mallet, I figured I'd let physics help me out a bit..
I hit the spindle several times hard and applied some force to the tie rod end, as was suggested, but it didn't move. After hitting the spindle I then gave the top of the tie rod end about 3 or 4 hard taps with the mallet, the tie rod end I have has a "buffer zone" on top without any thread, so it was safe to tap it, but not too hard. After that it fell out. It looks like the step I missed was hitting the spindle, that seemed to help dislodge the tie rod end.