I'd like to be able to control everything in a particular room without having to switch back and forth between "My Scenes" and "My Devices". Is it possible to show both scenes and devices simultaneously when viewing a particular folder?

I'm not aware of a way to do that. You may be better off adding the scenes and devices that you want to see to the Dashboard, where they're all shown on the same page. But you'd lose the folder structure.

I'm thinking a workaround could be to create scenes for all my devices, even ones that aren't currently in scenes. Instead of directly controlling the device itself, I'd just control the scene instead. At least that way I'd be able to see everything I want to control in each room all at once.

With ekeypad and you can accomplish what you want.