I don't think there's any way around it as it probably has to re-interpret the entire file from scratch when changes are made. What I've been doing is splitting my character animations across multiple files using the Link feature in Blender so that any changes to the base file propagate to the others. Another tip is that if you're using modeling modifiers like subdivision it becomes tedious for the FBX to interpret all of the animations, so my split files have some modifiers disabled so that the work is easier. In other programs this can be done by using a lower LOD version of your model. This is possible because the only thing you care about in these split animation files is the rig/keyframe data itself.