This is rather vague ("only the first few items load in the overlay" - is that the page cutting off, the content being missing, a white space, etc etc), a screenshot would have helped.

Ok I can reproduce though thankfully. It is the overlay space not resizing due to JS cross-domain permissions.

This is not fixable without a couple of weeks work.

JavaScript does not allow cross-domain iframe contact, and logins won't be shared anyway. Even with CORs or other modern HTTP techniques. The only solution would be to re-engineer all helper script calls to be able to reside all the multitude of domains and re-engineer the JavaScript to point the calls appropriately.

The zone base URL feature was originally intended for putting out very custom functionality or content across different domains, it wasn't intended for putting full CMS interactivity across domains without significant custom development.

The field label for the zone base URL zone option will include a note about the limitation of this option.

I would generally advise to keep a site from excess complexity, running a site across multiple domains would generally be something only a company with many full-time employees should be aiming for - there's a lot of complexity for it, and not a lot of real need.