Aww poor Gizmo,
I think you did right by picking him up AFTER the Sheppard grabbed him the first time, but I also believe that the instructions to not pick up your dog is correct too, but ONLY prior to any dog making contact with each other. IF, they are only snarking and claiming space, then yes, leave them be but watch carefully or perhaps leave - if it was your dog that started. We know you already know this Nerdy…- in general for other owners.
I know everything happened so fast and read that the Sheppard owner is generally mindful and we know that you are careful as well, but when you think about it, your instincts were right by picking Gizmo up after the initial attack and I'm sure he is grateful for that. If anything, the only thing that I would do different is to chase the other dog away to let both dogs know that it is the two legged creatures that rule the park. If any of the owners had an issue with me doing this then I would say "Then watch your dog, so I don't attack him." Amazing how that phrase gets them every time...
I'm not sure if your park has a governing body that supports and cleans the area, but our park has a member / volunteer committee. When Kairoe was attacked at our park, I spoke to the committee and they set out to speak to the owner, last I heard the owner has not been back to the park since her dog was much like the Sheppard and had a reputation. We pay a nominal fee of $5 annually, to keep our parks alive. This fee is for entrances to all dog parks here in Mississauga. We enjoy our dog park and fully support more dog parks, simply for the reasons that it's for the dogs and it lets our City know that dogs have a voice when it comes to voting. Further, by posting that sign you will also enable more owners to identify the bad owner and perhaps have the owner at least be more mindful. Hopefully, his pocket will feel it too.
Keep ya heads up.
Emm