I documented my prior attempt but the results weren't great. Here's the summary for historic purposes. This is my first real electronics project so I wanted it easy. I used an Arduino with an HC-05 Bluetooth module reflashed with RN-42 firmware, and Sketchup for the phone case modeling. The HC-05 worked but I don't think that reflashing the firmware is appropriate for a community project. Sketchup was entirely inadequate.

I ordered parts, breadboard components, and soldering iron. I learned microcontroller basics on the Arduino - blinking LEDs, voltage dividers, button input, debouncing buttons, pull up / pull down, bitpacking. The Arduino was great for learning that. I re-learned soldering which I haven't done in years, and breadboarding. Pro tip, don't buy bottom of the barrel jumpers, half of mine are dead and it caused endless frustration.

EEVblog how to solder:
https://www.youtube.com/playlist?list=PL2862BF3631A5C1AA

Concepts and mindset of soldering:
https://www.youtube.com/watch?v=vIT4ra6Mo0s

I had the parts ready when mitxela's guide appeared on HaD so my HC-05 attempt was based off this guide:
https://mitxela.com/projects/bluetooth_hid_gamepad

I got the controller to show as an HID gamepad in Windows. This is where I stopped with the Arduino/HC-05 and ordered nrf51822 gear. It can definitely work, I just don't think it's ideal.

Here's the phone case I started for my Nexus 6P. My friends and I had already been using Sketchup for other projects however it turned out to be a poor choice for small models - I had issues with keeping faces flat and with Sketchup combining nearby lines.

My new attempt is using the nrf51822 BLE SoC and Fusion 360. I got nrf51822 compiling and flashing working but no code of my own yet. I've made great progress with Fusion 360, parametric modeling rocks. More updates to come.