Well, let me see if I can figure out what you're attempting.
Are you saying that you have a page that references a request-scope bean that's created by cloning data from an application scope bean? And that, if the application-scope bean's data isn't valid for that request that you want to instead display an error page? And that throwing a FacesException in @PostConstruct is too late, because the page is already rendering?
Probably the cleanest solution is to check BEFORE routing to that page in the action processor that sets the new page and its new request object up. If the data isn't valid for the request, redirect the action directly to the error page. Plain-vanilla
JSF, no special magic required.
That, of course, doesn't work if someone attempts to access the request-bean page via direct URL request. For a case like that, I suppose that one approach would be to use a Filter and verify the session bean data in the Filter. Redirect the URL if the verification fails.
Access to the actual request bean isn't necessary, since beans aren't directly addressable in any case, and especially at request scope where they have no existence outside the URL request/response cycle. Although I might put a static validation method in the request bean if it makes sense from a "keep-everything-together" point of view.
Another approach, if you're looking for wiring flexibility would be to inject the application-scope bean into the request bean, have the setter verify the required properties, and throw a FacesException if the properties don't fit.
You very probably will see an undesired URL returned to the client's navigation bar in many of these cases along with the error page. A solution for that is to subclass FacesException and create a custom error page (which is better than a standard stack trace, anyway). That page would then have a link back to the application mainstream. It won't fix the URL, but the important part from the user's point of view is that the application will have a smooth flow of control and not be thrown into esoteric technical displays. And, if you're really obsessive about the URL, you can probably make the error page forward. But it's probably not worth the trouble.