The bandwidth isn't really the biggest concern. It would be easy to move the downloadable video files over to Amazon S3 or another CDN.
High CPU and database usage is almost certainly due to poor programming in the blog and forum software, and these could mostly be fixed by enabling content caching. The blog itself should essentially require zero database accesses once cached because there aren't thousands of comments (you can just update the cached copy when a new comment is posted) and there's no user login facility. I can't think of any reason not to enable very aggressive caching in Wordpress in the EEVblog's case.
I've never administered an SMF installation, but it looks like it has some basic caching facilities, but these require the use of a PHP accelerator which the host may or may not support (most of these are commercial software, so it's unlikely that you'll get it on a shared server). The options are to rewrite bits of the forum to be less horrible (not trivial, but it might be a fun exercise) or move to a high-end virtual private server (not a $10/month one) or a dedicated server, or switch to a better piece of software.
In Australia, two of the largest forum sites are Whirlpool, which uses completely custom software, and OCAU, which uses vBulletin, which is commercial software but not especially expensive. Most of the huge international forums seem to be using custom software.