Sorry to bump in like this... I've been reading this and kinda thinking out loud....
Since you're willing to spend like $500 for a custom made joystick.... maybe as well... whoever is making it can do it right....
so far, you have not been telling us much about your friend who is in wheel chair....
personally, I don't know anything at all about analog stick... but the least we can do design-wise on the stick is to know how he plays....
does he always sits on wheel chair when he plays ??
or always a sofa ?? or bed ?? etc.... if there's a steady place he sits, maybe we can design it with a particular size so that it can sluggly fits (like to his wheel chair) and not on his legs... (just an example...) or if he plays in bed, then maybe a simple platform so that it curves (or angles) around his body... (or something...)
also, if his arms movements are not as good as normal person... (sorry... no offense to your friend... but I'm just guessing different sinerios...) maybe he might want the joystick to be a step down so that his wrists can hit the button easier... (more convinent for him....) or if he can't use 2 sticks.... then buttons might need to be arranged... or use trigger sticks so that his wrists don't need to hit so many buttons ?!?!
I mean.... these kinds of design issues... we won't be able to guess unless you tell us his "exact" situation....
Although I don't have the knowledge to build this thing, if you let us know the situation, maybe a few of us here can chip in some ideas to help..... (you know.... after seeing 1up's cab.... I KNOW... there are a gang of geniuses around in this forum.....)

so.... if you and your friend don't mind, can you post some details ??