Yes the thin plywood method and towel is good, hard work but effective. Last time I did it when I pushed the fridge back against the wall I cut a perfectly sized bit of plywood that pushed against the skirting under the fridge so that I could just push the fridge back into position over the plywood.
Provided the appliance still has its rubber feet, you can slide it out on a lubricating film, such as washing up liquid and water, WD40, or furniture polish.
I favour the detergent because kitchen floors, especially under appliances, are often dirty, greasy and sticky and the detergent cleans it off.
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