I wouldn't use the thumb stick as it is. Rather, I'd put it in a controller and use the thumb stick as a means to mimic the pots on a real controller. If I ever get around to making a mini-yoke I'll post info on it.
Honestly, if you want to mimic the real thing, I'd try to get a used yoke from star wars or other machine. They can be had for a reasonable amount of money and you won't have to sacrifice too much.
I havent seen a used star wars yoke on sale for a while, granted I havently actively been looking in the last year or so, but they were rarely under $350. I have seen some refurbs and/or reproduction yokes for about $600 recently.
The parts for the encoder and accelerometer are $30. Worth a shot for that price, I have alot of the other parts laying around that would be needed to make an attempt at a yoke. So very little expense for an experiment at this time. Will give it a go I think, it will probably take me a few months to actually do anything. Always lots of projects I want to do, time is usually the problem.