This isn't going to work the way you think it is, and @Jen Roberts instincts are right.
For a user to see a Confluence page, they must have read access to the space. You need to set up the spaces so that they all have a public and private sections, so that your user can see the right pages, and then restrict all the private areas in any spaces you've let the user see.
If you don't use anonymous access, you'll need to have a user who can see the spaces and then public pages. People logging in as that person will be able to modify the passwords and account settings.
So, on to your API suggestion - yes, that's the only way. Have a read-only user, then write something that scrapes the pages you want to publish over REST and load them into another web-server as static pages (consider a regular refresh).
In my experience with the Confluence Cloud, this request would need to be done manually - meaning each page would need to be set - Restrictions/Access (any open Spaces would need to be set to Restrictive as to keep the Said User outside).
I'll be following your question as to learn if other options are available!
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