why not. create a replica of the PSP case with a silicon molding material, then modify said replica to house the extra part, i would place mine on the upper part of the left side of the case, where it doesnt interfere with the shoulder button triggering, so a little bellow the shoulder button but above the D-pad
then the modified case can be replicated once again with a hard resin, you can even go the extra mile and make the analog stick vessel dettachable, i was thinking the wrist-strap loop could somehow be used for this purposse.
i have experience with modding Warhammer:40K miniatures this way, as a matter of fact most of my armies ive casted myself
here are some supply sources:
http://www.smooth-on.com/
http://www.polytek.com/
P.S. it isnt cheap