I understand that a page requires a minimum number of words so that google values the page. Does this really apply to the homepage as I have no end of well placed competition with no more than one hundred words on their homepage? We offer English language courses and my students have commented that the homepage is too wordy. All 400 of them!!
You mean 400 words of content on the homepage itself? I think that's ok and nothing wrong with that. In fact, I was about to suggest 400-500 words.
Content is king, the more content the better. There is no specific amount of content you need, but you want to use content to proper describe your website. On the homepage this is a major issue, you should use content to describe your site\services and use that content to internally link to your web pages. It's not common with a site with less content to rank better in search results, backlinks and other on-page factors also are taken into effect.