I managed to find a solution by modifying the Three.js source. Inside the THREE.Animation.prototype.update() method I replaced
vector.x = vector.x + ( currentPoint[ 0 ] - vector.x ) * proportionalWeight;
vector.y = vector.y + ( currentPoint[ 1 ] - vector.y ) * proportionalWeight;
vector.z = vector.z + ( currentPoint[ 2 ] - vector.z ) * proportionalWeight;
with
var xOrig = this.root.position.x;
var yOrig = this.root.position.y;
var zOrig = this.root.position.z;
vector.x = (vector.x + ( currentPoint[ 0 ] - vector.x ) * proportionalWeight) + xOrig;
vector.y = (vector.y + ( currentPoint[ 1 ] - vector.y ) * proportionalWeight);
vector.z = (vector.z + ( currentPoint[ 2 ] - vector.z ) * proportionalWeight) + zOrig;
This only applies to the X and Z axis, which is all I need for my specific application. However, this doesn't seem like the "correct" way to solve the problem.