Something a lot of people fail to notice is that the Content area is a region; you can place blocks there. If that's not enough, many themes already have a Content Top and Content Bottom region; if your theme doesn't creating a sub-theme with those regions is not hard.
I wanted to follow up. Nancy Wichmann's solution is perfect. I used EntityFieldQuery to get the nodes and I had to use custom code to produce the blocks, but the home page is now working perfectly.
Thank you.
Fred