Whirlpool washer tub noise on spin cycle

Hi. I have a Whirlpool direct drive washer (LSR7233EQ0) that makes a
noise on spin that sounds like "zzzzp, zzzzp, zzzzp", which gets
louder as it spins faster, then a loud "CLUNK", then it starts the
zzzp zzzzp noise again. The top of the agitator moves about a half-
inch side-to-side while it's spinning - i.e., the path of it's
spinning inscribes a circle about a half-inch larger in diameter than
it is (does that make sense)? If I physically hold the top of the
agitator, allowing it to spin, but not wobble, the noise all but
disappears (and there's no CLUNK every so often).

Sooooo, I think it's probably something in the tub's coupling to the
drive shaft, the drive block, perhaps? Does that sound like a likely

I need the spanner tool to get the tub off, right? Is there any way
to substitute for that? I tired a hammer and stubby flat-blade
screwdriver, but it seems to be on there pretty tight. I hate to
spend $20 on a tool I'll likely only use once (anyone want to buy a
slightly used spanner tool?). At least it's still a whole lot cheaper
than paying someone else to do it for me!