On a RAAF C130A, I was detailed to fly with the Wing Commander, to see how high we could get a C130.
The A model being the lightest of the C130 models, would have weighed at 55,000lbs plus crew and fuel.
So at the top of the climb would have weighed about 65,000 lbs and at 37,000 ft, she just would not climb anymore.
The boss said well now we know and we went home. A model only had 3750HP engines, in the E model the best I ever saw was 38,000 ft.
I think the problem flying the J model high, is your speed would not suit mingling with the jets.
Regards
Col Tigwell