Unfortunately, that isn't possible to do. Since all of your domains are connected to one store they're connected to one account platform. In order for there to be any differences to the home page, you'd have to change the image under a different theme customizer which would require multiple account platforms. I know that's a bit of a tongue twister, but does that make sense?
We have a discount option available for stores who have multiple accounts with us, but the only way that discount works is if the websites are exactly the same (including images) with the only difference being language or currency. Are you wanting to change the image for language reasons? Would this option work for you?
I'd love to provide you multiple workarounds, but for this particular question that's the only thing that could work.
I hope that helps to clarify. May I ask why you want a different image for each domain?
I look forward to speaking with you further,
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