Well, I don’t really know why I didn’t make this work better quite a while ago. If you need flexibility in your page layouts and you use a lot of Views, then I believe that this is the way to go. Use Panels for the overall layout and then plug in smaller bits of content within the Panel locations using Minipanels. I tried using them before and I think that I simply made a couple of mistakes in implementing them. But now that I know a little more than I did before, I have used them successfully and their implementation is going to be a real Godsend to me.
Here is a little image of what you can do. The layout here is a standard AT_Core layout that I have subthemed. I used Minipanels to add the smaller black boxes in the layout. Now I can have two elements at the very top of the page without having to use so much CSS that I run into other problems later, especially when I view the site on a mobile device. And the page is all Panels so there is a lot of consistency. The only issue is that I have to edit the Minipanel separately from the rest of the panel page.