When having a short circuit protection circuitry always simulate and record behavior of the short circuit protection circuit during dropout mode. Make sure that it does not turn ON during dropout and increase the dropout of the LDO especially at corners.
Make sure if the LDO is enabled immediately or if the supply is applied immediately the output current still is controlled by the short circuit limit protection and does not fly uncontrollable. This means the short circuit protection circuit must always be enabled first and allowed to settle before releasing the output FET for operation.