I too have a speed queen aws44nw washer that made noise during the spin cycle. I removed the front cover and checked my springs, also pried up the tub module to make sure the white friction ring between the machine base and bottom assembly was o.k.My machine is level. I then removed two screws for top cover and tilted it back. Remove fabric softener dispenser and then agitator by rocking it back and forth while pulling it up. Remove tub cover by prying snaps back then lift off. Once the agitator is removed you can look straight down through two drain holes at the bottom of the stainless steel tub. What you are looking at is a white plastic piece that speed queen calls a filter. Mine was all gunked up. I removed the bolts at the bottom of the stainless tub using a 13 mm socket wrench setup and lifted the tub out. I then used an old toothbrush and cleaned this filter out until I could see through all the little holes. Clean everything up during assembly and machine will spin great. I suspect other model speed queens have a very similar filer.

The machine is probably not leveled properly. To level the machine, partly fill it with water. Make sure that the drum is standing in the middle of the machine and then adjust the machine until the water is at the same level all around at the nearest set of holes to the water. Check that the drum is still in the center of the outer drum. Make sure that the adjusting feet are all firmly on the floor and that you cannot rock the machine at all by hand. A top loader must be 100% level or it will shake.