Is this the case for logged in people as well as anon (non-logged in)? If so, that points towards a bit of a fundamental issue which shouldn’t be affected by domain or subdomain fiddling.
In our instance, we definitely do want to have Discourse in the root domain as it is the absolute centre of what we do. So I too have been looking at how best to optimise /admin/customize/site_texts/login_required.welcome_message and the other elements of that page.
The good news is that you can use all the usual Markdown, etc in that text; this allows a lot more flexibility. I achieve this by writing it in a topic in #staff and then copying it into the customise bit. @codinghorror - it would be extremely helpful for people in our situation to have it behave the same as the FAQ etc pages instead.
Also, you can provide links to the Privacy and TOS pages (which should be visible to anon users) using the Custom Header Links Theme Component (with some extra CSS). Of course, I’m not happy with that and want anon to also see the FAQ and About pages (while keeping the forum private) so have asked for some help: