It is my understanding that the available short circuit current calculated with the percent impedance voltage of the transformer is based on an infinite supply. As a result it is a conservative figure.
If the 13,727 amps is at the transformer secondary, there may well be enough impedance in the conductors to the main panel to get below 10,000 amps, if that helps.
If the 13,727 amps is at the panel, that's the figure that you have to work with.
Another option may be to add series impedance to the feeders to limit the current. I don't know if they are still on the market, but at one time wireless reactors were available. This was a bracket and a stack of cores on the front of the transformer through which the feeders passed. They could add several percent impedance to a circuit. Be aware that as you reduce the available bolted fault current, the voltage regulation will suffer in the ratio of the change. You can probably accept the change.
respectfully