Minimizing Paint.NET send the app in a "low-profile" mode. Notice that the title change from Untitled (100%) - Paint.NET ... to Untitled - Paint.NET ....
So that's basically what you suggest.
You can also remember to hit Ctrl + D when you paste a screenshot, if you use the Ctrl + V keyboard shortcut, the keys are very close to each-other.
Also, I'm sure you'll be glad to hear that the next Paint.NET version is developed and re-factored with performance in mind, even in low-end, single core systems