Answer based on information found on-line. Related documentation:

C-130J Hercules
Source: Flight Global
The KC-130 Hercules is the tanker variant of the C-130 Hercules. The cargo opening consists of a door, and a ramp which can be operated separately.
- The door is opened by rotating up and inwards the top panel.
- The ramp is opened by rotating down and outwards the lower panel

Source: CQ Planes Spotting
KC-130 / C-130 have a good maneuverability at low speed.
From the the C-130 flight manual:
- Door and loading ramp are operated at a speed of 150 KIAS, with flaps down at 50%.
- Same conditions for flying with door and/or loading ramp open.
Low speed adjustments:
- Reducing speed from 300 kt to 150 kt requires nose up trimming.
- The center of gravity may be adjusted by ballasting fuel in the tanks (refueling tank and aircraft tanks).
Opening the ramp will change the aerodynamic shape of the aircraft:
- The ramp will not be moved past the horizontal position (only need for full down position is to load cargo on the ground).
- Moves the nose down.
- Balanced by some trim accordingly.
If loads are dropped (pallets, paratroopers) or fuel is delivered, the center of gravity will roll back, with a significant nose-down tendency, and trimming will be required.
Opening the door will be less of an issue as seen on the image below:
- The aircraft is near level.
Above: KC-130J Hercules (source: Military.com).
Note that the attitude is not so far from level, in spite the door is open.