The firing pin is indeed held in place by a pin in the Uberti design; I don't know the details of the Pietta design:
One could certainly open the frame hole, remove the OEM firing pin, and fabricate, heat treat (harden) and install a new firing pin.
I don't think it's ever been claimed that it was impossible to modify the gun to use a regular Colt cartridge cylinder, but Uberti's design was likely intended to move such modification out of the realm of the home hobbyist. Breed's simple mod with a file may well fall in that category, while fabricating and installing a new firing pin and opening the frame hole perhaps would not. If I were a UK bureaucrat charged with seeing to it that the citizens couldn't defend themselves I'd take a serious look at that simple mod with an eye towards banning the gun if it's truly feasible.
A couple of questions come to mind here: does one get reliable ignition from an edge strike on a centerfire primer, and likewise does one get reliable ignition from an edge strike (such as with the modified pin with the original offset cylinder installed) on a percussion cap? I don't know what to expect with those conditions.