My Corolla's vibration is not really evident at 40mph, but at 60 is
at its strongest, thouh it is present well beyond that speed. It is
annoying, but not enough to make me avoid those speeds. It comes
through the wheel and body, not the brake pedal.

Yours is not:
loose wheelnuts
loose studs
loose/worn wheelbearing
warped disc
BenT wheel
out-of-balance wheel or tire
damaged tire
camber or caster (maladjustment wouldn't do this)

Could it be your:
Balljoint?
Possibly a radius-rod/steering-rack balljoint? I've never heard of
this being a cause, but if these
          develop  a harmonic it might just possibly cause a pulsation.
Stiction, with or without wear, in the steering rack?
Worn suspension-arm bush?

It SOUNDS like the wheel is ot lonitudinally fixed, and so is rocking
back & forth (left-right). Can you drive it while someone looks out a
window at the wheel to see if there is visible movement, and if so,
in what direction/plane?

Sounds like I should be trying these things out myself...
--
Andrew Grebneff
Dunedin
New Zealand
Fossil preparator
<andrew.grebneff@stonebow.otago.ac.nz>
Seashell, Macintosh, VW/Toota van nut