The comments in post #2 agree with my experience.
The supplied lens is reasonable for the intended purpose. The main difference seen due to different focal length is different magnification for a given projection distance (lens to screen).
The focal length is chosen to accommodate the projection distance and magnification wanted.
At a projection distance of 6 meters (about 20 feet) the 12” lens gives 18.7X. With the 14” lens you’d get the same image size at just under 7 meters.
My Beseler MF slide projector uses a cast and machined aluminum lens mount. The barrel of the lens is gripped in the aluminum mount with a setscrew making it easy to change lenses. Mine is 10” focal length.