Jay--
You'd do well to consider the unique operational squeal of your White-Westinghouse a part of its charm and character. Nothing says "I love vintage appliances!" like the floor-shaking thunder of a Frigidaire 1-18 or the sub-woofer-like growl of a mid-60's GE Filter Flo.
We take pride in yelling litanies of interesting facts to startled friends in our kitchens as the vintage KitchenAid dishwasher roars deafeningly in the foreground.
To alter such eccentricities is analogous to painting over beautiful woodwork or laying lime green shag carpeting (you stand accused, Mom!) over hardwood floors.
So, next time your washer kicks into the spin cycle, savor that raucous squeal as if it were a fine, aged wine. Or you can check to see if the belt is slipping.