So I got that stupid thing changed out. It was not easy to get it out. I had to knock the snot out of it to get it to come off. 2 hours to get it off, and only 7 minutes to get it back on. Not a terribly difficult job, but took a lot of elbow grease (and shoulder grease) to get the old one off.
I had first bought the tie-rod puller that has the jaws and the screw to pull it off. It probably would have worked fine, but there was no clearance above the center link to fit the puller onto it. I did get it onto the passenger side by turning the wheel, but I found out that the jaws were too far apart and it kept slipping to the side. So, I made a trip back to the parts store to get the one recommended by a few friends. The "pickle fork" type device. They aren't technically supposed to take returns on tools, but the guy that sold it to me was there and I explained to him that it didn't work. He found the one I needed (the fork) and I got $3 back for the difference in price between them.
A note about their loan-a-tool program. You have to get them from the front and ask for one ( a loaner) specifically. I'll do this next time, especially for something that I probably won't use ever again. This tool was only $10 though, so I wasn't too worried about buying it. Parts and all were still less than one hour of labor at a shop.
Haven't taken it for a test drive yet, (waiting on the weather to clear up) but everything seems to be fine. No movement in the steering system now.
Hopefully, I can adjust the steering again to get the excess play out of the steering wheel. I'll put it a procedure for doing this, with pictures even. I did this a couple of months ago to remove some of the play out of the steering wheel. I think if I do this again, it will actually help and improve the steering.
Total cost for this job: $60.99
center link (drag link): $38 (from autohausaz.com)
ball joint separator: $10
Other stuff I ordered from the internet to get free shipping on the main thing I needed: $12.99 (stuff I needed anyway, but didn't want to order separately)