Yes, it did move. So you mean the ~64 squarefront still had the potato on the drum shaft and the eccentricity I saw was the moving of the idler? I can live with that, far as reconciling geezer memory.
In the short time we owned it, required more service than both the prior slantfronts combined. Plus mom didn't like it and replaced with a Westy-branded TL seems was actually a latter-day Fridigaire. At which point my head was spinning and not necessarily balanced either.
From there on I had a FRIG humpa-humpa, several WP wigwags, Panasonic TT, couple classic MTs, and landed on Frig-branded FL that's really some Euro thingy but it's never busted. (Shhh, don't let it hear that last part, might jinx it.) And a Lady Kenmore 120V dryer since 1984.
Back towards topic:
FRIG humpa-humpa = Frigidaire with original vertical agitator
WP wigwag = the classic Whirlpool transmission that built WP's reputation
Classic MT = the Maytag auto that built their reputation
TT = twin tub, wash on the left, spin on the right (any exceptions?)
FL = front loader
Lady Kenmore 120V dryer = apartment size, with casters, plugs into a standard socket
Frig-branded Euro thingy = frontloader with Frigidaire printed on it but you know bloody well 'Frigidaire' didn't build it because by that time Frigidaire was only a name you could license and put on anything, just as Westinghouse is today