What do I need to mod a 360 TE stick to Xbox one?

I just picked up an Xbox one and tried Killer Instinct with the dpad on the controller and it was god awful. I could do all SF4 trials on the 360 dpad, but this thing was very funky.
Im no stranger to fine soldering and have done a rjtag and demon installs on a 2x 360s and smd leds, so controllers are a cakewalk.

You would need to dual mod with an xbone controller pad hack. There are a couple of 3rd party controllers to make things cheaper and easier. Should be no challenge to you with your stated soldering experience.

Xbone controllers: First wave of third party Xbox One padhack options

Dual modding tutorials: Dual modding 101

Hori Xbox One controller padhack and a dpdt switch to go from one PCB to the other and You’ll be set. The controller is like $40 and the switch $3. cheap if you can do the work yourself.