It is definitely not an issue of the hole size, as your 1 1/4" is already larger than standard (1 1/8").
I personally never had any problems using the happ supers for SF, though my primary sticks are now perfect 360s.
It very well could be the "roundness" of the supers that is hindering you, and you may find the more "square" action of the competitions to be more suited to your needs. They use a square actuator to hit the button directly on the microswitch, so you can feel the diagonals. The supers on the other hand use a round actuator to roll across levers that then press the microswitches, and that gives a very smooth circle.
I highly recommend the Perfect 360 controllers, but they are quite a bit more $$$, and if your issue is the roundness, they will most definitely NOT help you out.