HEY, STEVEN, I'VE A FIX FOR YOU!
I encountered the SAME PROBLEM in recently (Spr. '18) fixing our GE washing machine. I nor my very strong friend could remove the agitator coupler cap from the drive shaft = it was impossibly stuck. WHAT DID I DO? I CUT IT OFF WITH A DREMEL. The coupler cap is a cheap part (like $12), so it was/ is sacrificial. The trick therein was to be very careful not to damage the shaft --> I cut through the cap very close to the shaft w/ the Dremel, then used a hammer + chisel for the final knock-off.
After the coupler cap was removed, THEN I FIND THE HUB NUT ALSO IMPOSSIBLY STUCK! Not even with a spanner wrench could I remove the thing. MY SOLUTION? I CUT THE HUB NUT OFF WITH THE DREMEL, TOO. Same concern therein: I'd to be very careful not to damage the drive shaft. So I employed the same process: I used the Dremel to cut as close to the shaft as seemed prudent, then chiseled off the nut with a few hammer knocks once the nut was 95% cut through. As w/ the coupler cap, the hub nut is a super cheap part to replace.
HOW DID THESE PARTS BECOME SO STUCK, YOU ASK? My only thought was that the person who'd our washer before us (we purchased it secondhand) might have used excessive amounts of powered detergent. The excessive detergent that didn't dissolve during wash cycles got lodged up between the drive shaft and agitator coupler cap/ hub nut threads & made these parts impossible to budge (seriously, my friend and I used all the leverage/ lubricant we could muster/ creatively force). Just like how grit particles can fill the gap btwn any moving parts and then seize them.
VOILA! IF YOU CAN'T REMOVE IT AS EXPECTED, (CAREFULLY) CUT IT OFF & REPLACE IT!
** 1 - The first image below shows the agitator coupler after I'd completely pulverized & removed it from the drive shaft (I'm holding the remains last to be removed). 2 - The second image shows the hub nut after I'd cut through and removed it. 3 - The third image shows the newly installed replacement hub nut & inner tub base hub (the old tub base hub was completely corroded through & the need to replace it was what initiated the entire fix). 4 - The fourth image shows the newly installed replacement agitator coupler cap. **
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