Currently, the X-T1 still has an edge, probably even over the X-Pro 2 which for many reasons is not the camera that a sport photographer would go for.
Very likely the X-T2 will feature improvements in this area. Your X-E1 is certainly much slower than any even current one camera in the range.
Waiting a bit longer will certainly tell you if the X-T2 will deliver improvements over the current X-T1. It most probably will.
The real question is whether sport photography is the area to which Fuji cameras are being targeting their production. The introduction of the 100-400 would certainly let one think that they are woking in that area on the other hand they might have decided that this (like the cinema market) is an area where they don’t want to commit themselves to.
