My Amana washing machine spins the clothes instead of agitating them. Is there a cost efficient part that could be replaced?

I don't have an answer for you. But, by my posting a response to your question, I am hoping that one of the several fine knowledgeable in appliance repair people on this site takes notice of your question.

Mine was doing the same and I went to the repair shop and was told to replace the Clutch dogs.
You have to remove the agitator and the clutch dogs are inserted.
The whole process took about 5 minutes.
The package of clutch dogs was about 4 dollars.
I'm not an expert in washer repairs but it was an easy fix. Hopefully yours is as easy.
My washer is a Whirlpool though so I'm not sure if the same parts apply