I have an FX1 with the stock pump shoe and a 144 pump shoe on my bench, and both pumps, and have been studying this for some time now.
Relating to pump losses, the 144mm pump with a 122.5mm shoe will not be efficient. There is a large low pressure area immediatley behind the shoe, leaving the most important area of the blades, the tips, in a state of cavitation, principally for the first blade, that increases with RPM. Someone in another post mentioned that a 1% loss of efficiency in the pump was like a 10% reduction in HP. Not sure about the absolute numbers, but the theory is valid, and supported by all those who meticulously seal their pumps, grates, and ride plates.
You can improve this tip cavitation by moving the blades as far back toward the stator as possible, and milling the stock shoe to it's max (130mm's +/- 1mm). But it still will not be as efficient as the 144mm pump in the SJ hull.
What I can't tell you is how much better a lower efficiency 144 pump may be over an optimized 122mm pump for your purpose and riding style. I just know that the pump performance will not be nearly as good (mathematically - this is key) as the SJ unless you use the SJ shoe, and open the intake to match the shoe. The smallest diameter in a system is always the limiting factor on mass flow with an uncompressable fluid.
Perhaps in potentially charging a customer a small fortune for a modified pump and shaft, someone realized that the gain may not be worth it for most people, or the work required to really take advantage of it may be more than most people can manage. I would also offer that if the FX-1 is stock or lightly modified, the pump mod will do little if nothing more than the right prop, milled exit nozzle, and a cone in the 122mm could do for bottom end. Also, taking off a stock plastic shoe on a SJ is far easier than getting the aluminum stock shoe off the FX-1. On the FX-1, I don't think it's possible to remove the shoe without glasswork in an area that is difficult to contour and sand (been there, doing that). However, if you decide to try, a torch and a rubber mallet can be a good friend (keep a fire extinguisher close as well, resin burns).
I think that just getting the pump to bolt up and lining up the steering is the easier part of this mod (no offense to the pump converters out there).
But like I mentioned earlier, a 144mm pump with a 130mm shoe may still be better than the 122mm stock pump/shoe IF the pump is the limiting factor in your ski, and/or you are really after bottom end with a potentially significant sacrifice in high RPM performance, as the low pressure region in the 144mm pump with a 130mm shoe grows with RPM. I would most definately suggest that anyone considering this mod mill or port the stock shoe to 130mm's. And since the stock shoe is tough to get off, porting it with a dremel and stone may be best.
-Joe