Well I eventually got it. Jacked up the strut as high as my jack would go, wedged the tie rod remover in, then used a hammer on the end of it to make it work as a lever. (I freaking stood on the puller and it didn't move.) O_o
Hammer on the control arm didn't do anything, and I hit that thing pretty hard.
I did use PB Blaster. The ball joint covers are all jacked up. I'll have someone who knows what they're doing replace them after I'm done.
(I'm admittedly not the greatest mechanic, I'm more into driving cars rather than working on them...)
Thanks for the help.