The strut rod goes straight through the LCA, so it won't bind back there if you remove the nut. That gets you halfway home. I don't think removing it from the LCA will accomplish much, though, as you'll further bind the bushings with the rod stuck against the bottom of the control arm.
If it's still bound up front, I'd suggest using a pipe wrench on one of the bushings with the nut at the LCA backed off, semi-hoping that it's bonded itself to the rod over its 50-year history and the rod turns with it. I say semi-hoping because a stuck bushing is a different kettle of fish once you get the pin bore clear. You could also try double-nutting the forward end of the rod to turn it with a wrench, assuming you've got enough free thread... I'm betting not, though.
If that doesn't work, you could always cut one of the bushings on an angle (think Sawzall or air saw here--you probably won't get through it with a knife in a single lifetime), getting close to the rod itself then manually cut it the last fraction of an inch with a utility knife as to not damage the rod. Pull the bushing out (easier said than done) and the rod will just flop around. You'd probably want the rear nut tight during the cutting operation.
I'm assuming part of this repair includes replacing the bushings, of course... and if that's the case, do not use polyurethane on the strut rods. They're literally too stiff, and will beat the ever-living crap out of the LCA bushings ahead of the torsion bars--especially if you use poly in the latter location. Voice of experience here: the Black Bitch had maybe 15,000 miles on a complete front-end rebuild, using all poly parts because gee-whiz magazine articles. When I pulled the front end apart to transfer everything to the beige car, the LCAs were completely trashed. They were ovalled from the poly strut rod bushings not allowing any lateral movement of the strut rods, as Chrysler intended. Almost all those miles were on smooth Atlanta roads and freeways, too, not MI's "surface of the moon" pavement.
The only place I use poly anymore is on swaybar bushings and links. Everything else on the Valiant is OE-replacement Moog rubber, as it will also be on the Challenger and Imperial, other than the latter getting solid K-member mounts. There is such a thing as too much road feel.