Ok I'm going to go against the grain here re:calling the vet out. The area where this horse injured itself doesn't contain any vital tendons etc. It's a pretty meaty area, I've had a horse do similar (with a post and rail fence!), called the vet and all he said was keep it clean, purple spray to keep the flies off, bute her for the pain, and keep the wound soft with white ointment.
I don't think the OP is a bad person by any means for not having a vet attend. If the wound wasn't haemoraging then obviously the horse didn't hit any major vessels, and there is no point in stitching a wound like that as fluid would pool in the bottom of the wound and would need to be drained reguarly, causing more problems to the healing proess. Very rarely will a vet stitch a wound like that.
Clearly, the OP has doen a marvelous job of healping the healing process of this horse, as look at the last set of photos! There is barely anything there. Well done
Re: bullet vs injection. I would definitely go a bullet any day. I had one put down with an injection and it was the most horrendous thing I have witnessed in a horse. It was terrible, he writhed around for a few minutes and tried to fight the drug, the vet had to give him twice the normal dose to do the job. Never again. I've had 3 horses of my own put down since, one for a shockingly broken leg, and two of old age. It was calm as can be. The horse was there one minute, picking away at lucerne, and the next it was out cold. Didn't feel a thing it was that quick. No fighting, not writhing around.
I think this notion of putting a horse down by bullet being cruel is a very young and inexperienced opinion of someone who has never witnessed an equine in such a terrible state that they are required to be 'put out of their misery'. It is a heartwrenching experience to have to make that decision, and although shooting them sounds bad, it's not. It hits their brain and brain stem depending on where the bullet is positioned, and they die immediately. Injection affects their cardiac system and nervous system resulting in increased heart rate and thus increased respiratory rate. Unless the horse has absolutely no fight in him left, he will fight this drug will all his strength, dragging the process out for much longer than neccassary as oposed to being gone in the blink of an eye.