From what I remember from UnrealScript before 3.x this would be possible but would require a custom player controller/player pawn and/or possibly a a custom Volume.
Basically when the player initiates commandDrop, a trace can be performed to see if the player is on the custom moving entity. If it is, add the player to a non-collision list in the Volume. I believe the Volumes (which can be used as a moving entity) have a collision override. Basically, if an object collides with the volume, check to see if that object is on the non-collision list. If so, ignore the collision. If not, collide as per-usual.
You might be able to avoid the non-collision list entirely though and just call a function in the Volume when you get the reference to it from the Trace in commandDrop.
It has been awhile since I've touched UnrealScript though but from what I do remember, this is very possible.
Another solution would be to use the trace in the commandDrop function of the player controller and find the height/width of the colliding volume. You could then change the players location to just below the volume. For visuals, you'd have to set a maximum height for the Volume though, but if it was small enough, the small player stutter probably wouldn't be noticeable. You could also add a drop effect to make it unnoticeable. Like for example, an effect similar to Captain Falcon's "Falcon Punch" in the Super Smash Bros series.