The Editable image web part is not designed to be used inside another web part. You can separate the web parts; use the original Editable image web part and the rest of code in a custom web part.
If you need to use the Editable image inside your custom web part, the parent web part must:
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inherit from the CMSAbstractEditableWebPart class and
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implement the LoadContent and GetContent methods.
You can take inspiration from the Editable image web part:
~/CMSWebParts/Text/editableimage.ascx.cs
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