Further, search engines will take a 301 redirect as a request to discard the original URL and use only the new one for search listings and ranking.
That is exactly what I want to do. The forum doesn't exist on the subdomain any more, it's included in a folder, precisely because I want the domain name to benefit from any SEO which might be derived from it's content, not the separate subdomain.
So it looks like I only need the last one. I'll check it out. Thank you.