Did the exact same experiment except I tried with no restrictor, and NO SPRING! It was ok but not that great. (Trying to remember the not so great part as it has been a couple months)
Oh yea, the original controller would spin around the perimeter with no chance of centering, EVER. With the U360 it played OK, but I remember it being kinda....meh, because you would have to concentrate a bit on NOT letting the stick come off the perimeter or 'centering' even the slightest bit. This definitely took away from high performance 720 gameplay IMO.
Here is what someone needs to make, and it might work. A restrictor that only allows 360 degree travel along the outermost layer of the U360's 'throw'. Add the light or medium spring and you might possibly have 720 bliss!
I'll be waiting anxiously for someone to build that restrictor!