I like to play RPGs while I work out via Steam Streaming to a little netbook.
It took a bit of effort but I got 7th Heaven and modded FF7 running through Steam WITH the Overlay, Streaming, and Steam Controller support. So I thought I'd share my success and method for anyone else trying to do the same. (Note: I'm pretty certain that this DOES NOT enable achievements or anything else through Steam, but I didn't specifically check either.)
Obviously you should get 7th Heaven/Mods running locally without Steam first.
For Overlay/Streaming
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Then add BOTH the 7th Heaven exe and the correct FF7 exe for the mods you're running as Non-Steam Shortcuts. Once you've done this, launch the 7th Heaven shortcut and click "Launch Game" and it should work like normal. Steam will recognize that another exe launched and "switch over" to FF7 more or less seamlessly. It's a little out of scope to talk about how to stream here, but it'll work the same as streaming anything else, just make sure you launch from the 7th Heaven shortcut.
For Steam Controller Support
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Once you have the above working, set up your controller mappings in the FF7 exe shortcut. I found it easiest to start with the WASD/Mouse template to start. You can pretty much set it to any keys you want, just avoid using any X-Input bindings. I made the grip button "Select" and "Cancel" and also setup "Ctrl + S" and Screenshots onto a touch menu for the left pad. (If anyone's interested I can post the text from the config file) The 7th Heaven shortcut should automatically use the default Desktop bindings, so you shouldn't need to touch it.
Once you're in the game, bring up the Menu (using the default controls), go to Config -> Controls and remap all the hokey numpad controls to your controller.
Obviously for convenience it's best to set up the Steam Controller to keys that you could actually use with the Keyboard to play too, or you could map the numpad controls to the Steam Controller directly and avoid having to remap them in the game.