If you look at the aircraft.cfg file you might find why you don't see any difference between the variants. They all have the same settings no matter E, H, J (KC,HC,LC,AC)
[TurbineEngineData] fuel_flow_gain=0.02 inlet_area=1.0 rated_N2_rpm=29920 static_thrust=158 afterburner_available=0 reverser_available=1
[turboprop_engine] power_scalar=1.0 maximum_torque=19600 ;H:maximum_torque(23030)
Not really sure how they came about these configurations for the maximum torque but all the C-130 legacy (E,H) models should have the Allison T56-A-15 engines, and the J has the Rolls Royce AE2100-D3
When you compare the older T56 models with shaft horse power you can see the difference. T56-A-7: 4,200 shp (3,133 kW) T56-A-14: 4,600 shp (3,433 kW) T56-A-15: 4,591 shp (3,425 kW) T56-A-425: 4,600 shp (3,433 kW) T56-A-427: 5,250 shp (3,920 kW) T56-A-427A: 5,100 shp (3,806 kW)
The 2100D3: Power: AE 2100 A/P: 4,152 shp (3,096 kW) AE 2100D2 and AE 2100D3: 4,637 shp (3,458 kW) AE 2100J: 4,591 shp (3,423 kW)
In regards to what you are seeing on climb out the difference in settings may be a place you look at (19600 vs 23030) on the maximum torque.
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