FCAC and stick leave behind a lot of flux shielding, and lets face it, a lot of over weld that can be a PITA to remove clean enough that you don't see it in the end.

But lets back step a second, and first off, need to be able to center drill the Device and the blind channel the barrel while not punch through the barrel into the bore.  Hence DRO to first find center, and the drill by DRO so you not over drilling the channel in the barrel too deep.

Next comes filling in the top of channel once pinned, and again FCAC is not the way to go.  Mig is a little better since you are using an argon shield instead of flux, but can still end up with a mess since mig can still end up with splatter as well.  So Tig is really the best option, since you can cleanly fill the channel over the top of the pin, without leaving a mess that will require a great deal of clean up in the end.

As for tig welder, basic scratch start tig would work, and if push can to shove, such a welder for such small work, could be set up for less than $150, including a small tank of argon.  
The mini toaster oven welders will give you about 110V on 220 cranked all the way up for scratch start that run about $50, manual mini  turn button sheild tig torch kit with lines will run about $50, and then this leaves you $50 for a mini disposable argon bottle and  regulator since you only need to run a micro Cup (4 or smaller), for the small area you are working.