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I'm going to offer you some possible solutions because I don't believe you will be able to find a new part from any of the usual suppliers.
I remember the handle and the consumers did not really like them. So, they were only around for a couple of years.
1. Have you tried calling 1-800-GE-CARES. You will need to speak to someone who can act as an advocate for you. I would go to their customer relations (or support) department and explain your desire. You need to let them know you are GE customer for many years and need their help with this.
Although, these handles are not in production it is possible that someone who knows how to navigate GE's immense inventory will be able to find either the exact replacement OR a similar handle that will fit on your refrigerator. It could be sitting in some parts warehouse in Alaska! NO GUARANTEE. However, we have had luck with this approach before and found parts that were not in production for years.
2. You need to reach a large population. E-Bay used to have an area that you could list an item that you were looking for. The other area would be "Craig's list". What you are looking for is either a new part or (maybe) one that was used but in good condition from a defunct refrigerator.
I realize that these solutions are not a complete answer and only represent a path to follow. So, please do not accept the answer unless they lead you to your goal. You can always come back.
I'm sorry. That was my mistake. I remembered that GE was the first to have these handles.
I thought this was a GE. While checking the our suppliers I used the model number and did not notice any reference to the manufacturer.
Whirlpool now owns Amana. Amana is still the website to go to. Give them a couple of days they have been good getting back. They just need some time.
They also have a huge inventory of parts everywhere.