In truth, goodman and amana are both owned by parent company Daiken.Fyi, Goodman owns the Amana brand. I installed a new furnace and AC some years ago. I ordered a Goodman system off ebay. The furnace was out of stock so they subbed an Amana unit. It had exactly the same specs and size. The paint was different.
Hard starts are commonly added to older AC condensers that dont want to start. They add an additional capacitor and voltage sensitive switching relay to help start the motor. The capacitor is switched out after the motor starts.
Hard starts are not expensive.
Yes, goodman does have some models that are identical to amana.