I know it may not be the best way to do it but i have always used a piece of 2x4 and a rubber mallet and hit the tierod upwards till it was out.
Oh and on changing the alternator , you are doing it the hard way by removing all that stuff. It can be done with leaving everything in the but its a lil difficult. I have done it 4 times and its still a chanllenge each time, but it can be done with the right extensions, swivels, and sockets.
