I feel your loss, having lost a dog recently myself. For the dog... I've given this a lot of thought and please hear me out. I not so sure that I wouldn't want to go out that way, think about it. You are doing what you love , what you were bred to do, the very essence of your being is to hunt and run. Your last conscious thought is of the prey in front of you... then nothing, maybe impact, perhaps a flash, a brief moment of unexplainable pain then peace. Gotta say man that don't sound like a bad way to go. But for the living, the witness it SUCKS.
I"m not trying to belittle your loss in any way, just put in a different perspective to help ya through it.
Prayers.