Better position yourself with your free arm on the side of the drop
1° Lean as much as you can into the drop, bending at the waist and lowering your free arm over the gap to lower the height.
2° Hop the tire off the edge by swinging your free arm up, rather than by jumping mad. That makes a very small hop.
3° In air, extend your legs and let the uni realign itself under you. Flap your arm down to absorb some momentum.
4° On impact, bend at the waist and tuck the seat against your chest, roll off immediately to absorb the shock into motion.
Dropping off sideways on the side of your free arm is easier as you can use your free arm better to smooth out the move.
See the move in a video
Lower your center of gravity
Basically, the main trick to limit landing disasters is to lower your center of gravity as much as you can before the drop by crouching and nearly leaning into the drop with your free arm and bending at the waist. The lower you can crouch, the less height you end up jumping off, and less harsh will be the landing. Holding the seat-in-front (SIF) helps a lot as it gives you more room to crouch without upsetting your precious flesh, especially during landing.
Counting pallets, splashing oil.
For some style, you can give a twist to your drop-off, landing 180 degree in the opposite direction. Build up the rotation with a large swing of your arm, like reaching behind your neck during your take-off impulsion, and then complete the rotation in the air, by re-adjusting your hips and the uni before you land. In air, flap your arm back down in front of you to help complete and stabilise the rotation.
Rolling off from a drop-gap
On impact, hit both pedals flat, but don't stall unless you jump from a low height. Instead, roll off immediately like in a rolling gap. Damp the impact by pedalling off rather than stopping flat out (your crank will thank you for that). Always land with both crank arms aligned to the ground but quickly push on your good pedal to roll one or two turns. The speed at which you roll-off will determine the efficiency of your shock absorption (converting linear kinetic energy into a rotational kinetic energy). Also, if you can, combine the pedalling with a progressive crouching, pulling the seat in front for extra mobility and resisting with your seat-holding arm to pump out some of the impact until the seat reaches your chest. Keep control of that pedalling, else the unicycle will shoot away from you and you'll end up on your bum.