Taken straight from the Alenia site
Maximum AUW 70,105 lbs Take off length 550m or 1806 ft
landing at 66140 lbs which is maximun length 1067 ft
Whilst I have crewed a C130 which went close it was not a C130J and one would consider it unlikely to be achievable unless all the cargo was the crews lunches.
As you would know I am a fan of the C130 but for short field operations the C27J has the edge.
Regards
Col