Ge Profile washer wont agitate

So, I noticed the other day that my agitator wasn’t moving. I dove right in and took it apart. I got the basket out of the frame and the agitator off but I cannot get the agitator hub nut to budge. The agitator coupling seems to be fine, inside and out. I have a short video on you tube of where I am and what is going on. The transmission rod in the tub doesn’t exactly move freely, but I can spin it both ways and it feels like it catches here and there before I can no longer turn it.

Maybe you can help me diagnose the problems and give tips to removing the hub nut. I have been using wd40, vice grips, and a 16oz mallet.

youtube link
In the bottom of the tub is rust and gunk i removed from the hub.

You should check again why it does not agitate. I don’t use a GE but a Candy washer, but i think most of the washing machine have the same configuation. One time when my washer did not agitate, i saw the mechanic pulled out the agitator and checked the drive collar splines. With your GE Profile, i think you may try put straight up on the agitator, you will see the drive collar with 7/16 head bolt, remove it and pull of the collar. First before pulling it off, spin it if splines are stripped it will spin freely.

I’ve got the transmission replaced and the entire thing put back together and the basket is not spinning straight up and down. I damn near tore it all out and put it back together and its still not right. The inner basket is rubbing on the outer tub. Sounds and feels like its making contact in the front. Its not horrible and is working fine after one empty load and one real load. I just know it wasnt rubbing at all before i replaced the tranny.

Any obvious spots to check for a washing machine that isnt spinning "true" or straight?