Well first of all you turn categories of on the home page.

admin - configuration - layout settings

Categories - Always Show on Main Page
Main Page - Opens with Category

Both to 0.

What I think you will have on your main page then is just the header and anything that you put in via the define pages editor.

So, you can put the various boxes in by the define pages editor. Whatever code you have to produce the three images on the other page put into the define pages editor. You are only adding the three images so I don't think the stylesheet is really an issue.

By the way it was pointed out to me in another post that the way to style the main page is to apply all the required styles to the <div> #indexHomeBody. So , it is do-able.