Hi,
that's a bad solution!
Basically, what you recommended is the best they can do.
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Implementing the right 404 (and not a soft 404) was a right decision but surely, having a custom page which helps the reader and gives him some choices is better than just serving a random 404.
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In any case, every page should redirect to the most (new?) similar page that talks about the same topic. Sometimes it can be ok to just redirect to the homepage, but it's surely not the best option to redirect ALL the links to it.
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Very important: don't use the meta refresh delays. It basically doesn't do a server redirect so that you're losing almost all the link juice when doing it. Instead, do 301 redirect via htaccess so that either your site and Google know that the old page is now actually the new page you're redirecting to.
Have a look at this if you want: http://moz.com/learn/seo/redirection
It surely helps!