Rob,
Thanks, that does help better understand your conditions.
The light that is at the finish line, even at a stop less than the example, is going to be enough to create some ghosting, especially at the speeds your subject is moving. You can notice the motion blur on the white paw of the dog with the red.
You would have better luck if you can move up track a bit so that you are shooting the dogs before they get to the finish light area.
If you tend to do most of your shooting from the same spot I would suggest a couple of things.
Assuming there is not a reason you can't do it, I would use both of your flashes off the camera and mount them left and right of where you are standing with the 430 on your right. This will help keep their eyes from looking so odd and will help with how the shadows fall off the dogs and the background. If you have total flexibility on where you can mount the flashes, I would experiment and treat it like you would a portrait shoot to get the best overall lighting, albeit a portrait shoot with 60km models.
I suggest both flashes mainly to give you a bit larger area that is lit but if you can easily catch them in the light field from one flash, use the second to throw some light on the background or backlight the dogs to give them a different look that what others might be able to get.
Since you are also only getting realistically one shot before they are past you, I would suggest trying 1/2 power on both flashes with the zoom set at around 50mm (Not sure your exact options on those flashes) and adjust your exposure accordingly and see what you get. If you are still getting too much ambient, increase the power to full power. If 50mm is wasting light outside of your frame, zoom in more. The more zoom, the brighter your flash and it might allow you to remain at 1/2 power which will give you a much faster flash duration.
Personally, I don't think the shots you originally posted are bad at all in terms of ghosting. The dogs are flat out hauling so a bit of motion in the photo is not bad at all. I just don't care for the direct flash look.