How do I change my home page without losing positions on Google?

Hi,
I will respond you with a "general advice", it is quite difficult to me to give you a complete answer to your question without knowing the URL of your client's website.

First of all you said that your client is in the top 5 on Google for his top 12 searchterms.

Which pages are ranking in the top 5 ?
The homepage or category/subcategory/detail page ?

I think that if it is the homepage, it is probably because of the website link profile, so I think that is quite difficult to loose ranking with "minor" changes. Minor changes to me means: a few change in the link structure of your homepage or a few change in the content of your page.

But it's totally different if the website is ranking with category pages or subcategory pages..

In this case my guess is that if you are moving all of the link in the footer, the strenght of those link will be weaker, so the probability that those pages will rank will be lower (because they receive less link juice).

In general, I suggest you to think about your visitors first, and then about search engine: is the solution you are providing the best for your visitors ? Will this impact in better the user-experience for your users ?

If yes, go for it. If not, think about users first.

I think that a loss of ranking is acceptable if the overall user experience (and conversions) improve.

That is my point of view from an SEO perspective.

That said, I think that the more important thing here is what do you expect from this change and which goals are associated with this.

Which is the goal behind those changes?
Do you want to improve conversion rate?
Do you want to improve search engin rankings?
Do you want to improve user-experience?

Links in footers are supposedly given less weight be the search engines, that's fine for Contact, TOS links but not great for key internal content anchor text links.