https://gumroad.com/l/shift_animation_tool - you can buy the tool here
This tool is for:
Most effective - working with motion capture
Correction of moving animation without feet sliding
Shifting animation without feet sliding
Recalculating the animation from a different pose
Rotating the animation without feet sliding

How it works:
The tool looks for a selected animation layer
Determines which objects are in the layer
Determines how the objects moved with the layer and how they moved without it
Based on this data, calculates the shift
It works via acceleration analysis algorithm
In other words, the movement of objects is calculated in a way, that extra shifting in the layer would happen in areas where the object is moving in source animation

Using the tool:
Start the tool
Select feet, main control and pelvis (depends on a task, can be different objects)
Move them to a separate animation layer (the tool will work with objects on this layer)
Shift the object within the new layer the way you need…