I will give you one tip about the Amana agitator that'll blow your socks off. I take off my leather belt, slide it under the agitator bottom till it's in the middle, then I turn my face away and pull up sharply on both ends of the belt to remove the agitator. Works every time.
You would only need to remove the agitator if you had to take out the inner tub. Otherwise you can get to any debris from the top without moving anything but the cover.