If Redwood's retriever head doesn't get it out:
Could you get it out with a strong magnet (a rare earth magnet like Lee Valley sells) fastened to the end of an old speedometer cable liberated from one of the auto wrecking yards in your area? Maybe liberate two speedometer cables for $1 each and connect them together with one of those U-clamps made for small diameter aircraft cable to search for the tool deeper into your drain piping. Both copper and plastic drain piping is non-magnetic so you shouldn't have a problem either running the magnet in or pulling it out.
And, there's always the Hail Mary play of:
Phone up the carpet cleaning contractors in your area and find out which ones have a "truck mount unit" or an extractor with at least two 3 stage vaccuum motors.
The drain pipe on your washing machine will probably be 1 1/2 inch diameter copper or plastic. Fill the washer's stand pipe's p-trap with water and ask them to try sucking the water (and the cutter head) out of the p-trap with the suction of their vaccuum motors.
I have an extractor with two 3 stage vaccuum motors, and I've retrieved a lost earing and a dental cap from a bathroom and a kitchen sink p-trap with it. It will lift a column of water 130 inches at sea level according to it's specifications, so the 4 foot height of a washer's stand pipe isn't a problem. (However, the density of steel might be.)