If your gun has been fit with an Ed Brown beavertail, in addition to the frame being cut to the .250"radius, the frame tangs have been scuplted on the outside where the web of your hand goes. When those tangs are ground away, it removes too much metal to change to another .250 beavertail without welding the tangs. All the other .250" beavertails require less cutting away of the tangs than a Brown. The Kings and STI are very little different from a Brown, in that area.
You might try an STI competition one..I know on the widebody STI/SV frame..both the brown and the STI fit up on the radius and little filing is needed to do a final blend...other than that I think you are stuck..