Okay, I will bite. I will just tell you what I do, as I am not an ob trainer, but I know you are looking for some responses.
Sounds like you have a dog that is motivated to learn. Great!
I am a bit unsure if you want a drop on recall for fun and good training, if you want to compete in ob, or if you want it for some kind of safety command.
What happens if you just say "down" while the dog is comming?
You may want to start working all your commands (sit and down for example) from a distance first so the dog understands that commands are to be followed even if you are not right beside her.
So does the dog stay already? Give a sit command take a step away, tell the dog to down, mark/reward. Increase distance a baby step at a time. Strategies if your dog is creeping forward during these commands is to tie the dog back to something stationary or have someone hold the dog's leash/long line so they can't move forward and get the idea the commands are to be done on the spot.
Another idea is to teach the commands on a small raised platform so the dog learns to stay on it (therefore on the spot) for commands at a distance, then you fade out the platform.
To reward at a distance you can use praise (a release is enough of a reward for some dogs). You can throw treats after the good command (dog is released at first with the marker so can get their treat). I taught it by throwing a toy as a reward for the distance command.
So once your dog understands that commands need to be followed/ and will be rewarded even if you are not right beside her she will be able to understand to down after a come command. You can reward it as above.
There are other strategies for teaching this stuff, fun and motivating and other not so motivating but hopefull that gets you started.
If you search for it you will find other threads on this topic on this board.
On the e-collar. You have trained your dog to come, that is great. The next step in training is to distraction proof that training. Being around other dogs is a top notch distraction. You need to work up to it.
I would chalk the episode you mentioned up to handler error as it sounds like you have not worked to that level of distraction. I am unsure of your dog's age, but you said it is not often off leash so I am going to assume your come command is not worked off leash and from any great distances and certainly not while the dog is in mid chase.
As far as if you handled it correctly, I do not like to give my dog a command I
know they won't obey. If I had not worked come with those distractions I might have hollered a super stern all business NO as soon as the dog was looking like she was going to leave the property. I also train a "leave it " command to break prey behaviors.
If there was no danger to my dog or the other dog, I may have elected to follow after my dog without saying a word and just put it on a leash when it stopped at the neighbour's house. I then would have scolded MYSELF all the way home for giving my untrained dog the opportunity to get out of the yard
Sounds like a smart motivated dog to me more than willing to learn and obey.
Congrats on your very successful training up to this point