I'm no Eloqua expert, and I stumbled across your question yesterday, looking for a solution to the same problem. I think I've found a solution, at least in the case of the EmailInlineDeployment deployment.
In your question, you don't specify what type of EmailDeployment you're trying to create with your POST request. If you're creating the "EmailInlineDeployment" type, I found that I can specify the replyTo and sender by adding them to the "email" object inside the "EmailInlineDeployment" object (which you post as the body of your POST request). The "sendFromUserId" also needs to be set, but that id doesn't need to correspond to the replyTo or sender information. Something like this:
... other stuff here (including the htmlContent), omitted for clarity ...
"subject": "My Test",
"replyToName":"The reply-to name",
"senderName":"The sender's name"
I haven't been able to get this to work with the "EmailTestDeployment" type of deployment. I would imagine that since the email already exists in Eloqua, Eloqua expects you to have the correct ReplyTo and Sender set on the email object itself, prior to deploying the email. But that's only a guess on my part.
I hope this helps. If you can't get it to work, let me know.
The email sender name and address are contained within the Email Asset object (https://docs.oracle.com/cloud/latest/marketingcs_gs/OMCAC/op-api-rest-2.0-assets-email-post.html). You'll have to create or modify the sender details within that object prior to accessing the Email Deployment object. Hope this helps!