Your walking machine might be helped by setting it on a scrap of the "non-slip" shelf liner that should be available at most any big-box retail store. It's touted for RV users to keep the stuff from ending on the floor during travel, although in that application it usually just ends up on the floor, stuck to the bottom of the stuff that was sitting on it.
A "heavy duty" non-slip pad is also available at auto parts places for lining tool box drawers and such, and might help.
You could also jack up the front side of your counters so that the walkabout items all end up against the wall at the back, but that might be objectionable to aesthetic values.
Most such devices do have small "feet" that usually are intended to be a "non-skid" kind; and if yours sat for a time before you tried it, just washing the feet (or replacing missing ones) - and/or getting some of the slime off the countertop - might restore some of the "anchor capacity."
Most counter tops don't provide sufficient "edge" for using a large C-Clamp to hold down small appliances, but your's might be unusual so it would be worth considering.