Here is the problem:
The R1 is a pressure resistive button tied with a matrix kind of supply. In the same manner that the button on the matrix cannot simply be driven directly with a PIC output, the same goes for the PS3 controller.
Most PS3 rapidfire chips take the digital output (from either 555 or a PIC) and connect that to an analog switch. The analog switch can drive the 'pressing' of the button. What it cannot do is drive the 'releasing' of the button while it is already pressed. Thats why nobody has come up with a 'rapidfire on the trigger' as far as I know of yet.
Now, that does not mean this is impossible. Its actually very simple compared to some mods. What someone needs to do is cut the traces going to the button and wire them as a seperate input into a PIC. Then, wire the output of the PIC to an analog swicth, that would then drive the PS3 input directly. The PIC would then be programmed to drive the output normally when the rapidfire was 'off'. When the rapidfire is 'on', it would create the squarewave signal when the button is pressed instead.
The only real drawback is that it seems most controller coders do not own PS3s (like myself). I could draw up this code in an afternoon, and I have a 6-axis controller but no PS3 to test. I could always try the PC connection for testing I suppose. But my time is limited.
It also does not help that there are 6+ different versions of PS3 controller PCBs, and I can only comment on the 6-axis rummble contorller.