CoPress

I'm not aware of a plugin that will do that automatically, but I can think of a way you might do it manually. On our home page, we have three slots for featured forum conversations. To set those featured slots on the backend, it looks a bit like this:

I think one thing that you could do is build a plugin like this where you pre-define those 5 to 7 slots and then determine which tags they display with plain-text fields or drop-downs with your entire taxonomy. Changing what displays on the front end would just be a matter of updating the tags on the backend and then hitting "Save". Is there functionality you'd want beyond that? Do you have a mockup for what you'd want it to look like?

I think I built the backend feature in the theme, but it'd be pretty easy to translate to a plugin. I see exactly what you're thinking for the Hot Topics; it'd be pretty easy to do.

You can download the code I've put together to get you started. That will give you an admin screen to change the settings on the backend. When you update the settings, they're stored in WordPress' options table. To then get that information to display on the front end, you need to pull the settings from the options table and display the variables. It looks something like this:

To take the code I've uploaded and make it a plugin, you'll want to look over the WordPress documentation for the basic structure of a plugin. Once you get started, I'd be happy to answer more specific questions you have!