According to DerbyDad03 :

I'm not sure if this will work, but I'll throw it out there.

Are you familiar with the furniture/appliance slides that you can get
at borgs? (see the link below for a few examples)

Yes. But I haven't seen ones like those before. I was thinking
of the roller style appliance glides.

Have you used these things?

Did you see the warning?

EZ Moves Furniture Slides II's are designed for temporary use only.
Prolonged weight on the sliders can eventually damage the foam top. The
EZ Moves Permanent Slides are designed to remain under very heavy
furniture.

With vibration on a smooth floor they may walk about.

Permanently attach 2 (or more) sliders to the rear of the platform (or
stiffening sheet) and add spacers to the front to level it. Keep of
set sliders for the front nearby and use a prybar to lift the front
enough to slip the sliders under the front when you need to pull the
units out. The fact that the front of the platform will be on the
ground in normal usage should keep the platform from moving.

I was thinking of something like this, the main thing was ensuring
that it won't move in operation.

Yes, our washer does try to rebalance itself and does a moderately
good job of it. However, our experience has been with it being
more-or-less in the middle of a 14' joist span. A floor
lamp nearby (construction light ;-) sways several inches while the
thing is spinning, and carelessly placed things fall off shelves ...
At least it doesn't walk on its regular feet.

I'm assuming that simply placing it on the end of the floor joists
(immediately adjacent to concrete foundation) will solve most of it.
But I want to be _sure_ I'm not going to have to reengineer it
after it's finished.
--
Chris Lewis,

Age and Treachery will Triumph over Youth and Skill
It's not just anyone who gets a Starship Cruiser class named after them.