Widgets and pull-down notifications have been a part of Android for a very long time, but what if you combined them? Snap - Widget Drawer is essentially a second notification shade, but instead of notifications, it's populated with widgets. Plus, it's accessible from anywhere, no matter what else you're doing on the phone.
While Snap appears to be a system notification shade, it's actually an app that's overlayed on top of everything else. You need to grant it permission to do that on Marshmallow devices before you can do anything. As for older versions of Android, the setup process is more straightforward. Simply pick some widgets to add to Snap, and they'll instantly be accessible in the pull-down.
By default, you open Snap by dragging down on the right side of the status bar. The active area is about a third of the bar, and the rest continues to open your regular notification shade. The list of widgets is scrollable, and individual widgets can be scrolled with a two-finger gesture. The settings app can also be used to change how many rows and columns each widget takes up. It's actually surprisingly handy for things like Authy, which I need to access frequently while in other apps.
Snap runs a persistent notification, but it says you can hide that at the system level. I'm not sure if that will cause it to fall out of memory over time, but you can give it a shot and see. Snap is free for up to three widgets. Any more and you'll need to upgrade to the full version for $1.85.