Don't get after him. You will get him to start fearing a lead change.
It is hard to tell without seeing him but I would try this:
1) Stop changing across the center of the arena. You may need practice changing, but he does not need practice changing 'there'.
2) More collection. Drive him into the bit a little more. Sit back, drive him forward and 'bump' the bit if he speeds up.
3) Use a little outside leg to get a little reverse bend before a change. Then, your cue can be removing the leg as opposed to applying the new leg.
4) Do a change or two every ride from a counter canter on a big circle and lose the changes done across the arena.
5) When I am coaching someone, I have then go across the arena, change direction but not the lead until they are at least half way around the new circle in a counter canter. If a horse anticipate that change. I won't let them change then. I'll have them change the circle and direction again (keeping the same old lead) and come out of the corner and go diagonally to the opposite corner and change somewhere when the horse is collected and relaxed. The ask by applying the leg lightly that would ask for reverse bend and change with a soft cluck when the leg is taken off. You can avoid most of the 'tail swish' and most horses quit hopping or coming up behind with a change.
If you do not figure it out, just quit doing changes until you have knowledgeable eyes on the ground and good coach. Practicing bad changes really foul up good ones. Usually it is just 'over-riding' and 'under-collection'.