Me and my friend micro'd the hell out of this goose, but it just wouldn't die. We blasted it with all of a fire staff, and we had full log armor and battle helms on with battle spears, and it just wouldn't die. Has this happened to other people?
I suspect that, alas, you simply didn't wound it enough.
The wiki says it takes 58 hits with a battle spear to kill a Moose/Goose. But that's in regular Don't Starve. In DST, all boss monsters have doubled hit points. So now we're looking at 116 hits.
Similarly, 30 hits with a fire staff becomes 60...but you only get 20 hits out of a single fire staff.
Assuming you hit the Moose/Goose with every single fire staff shot (did you?) and assuming the fire staff was full when you started (was it?), you're still looking at 77 spear hits to kill the Moose/Goose...all while it keeps honking and making you drop your spear.
You might consider trying out the Health Info mod to help you see whether you're making any decent progress against it next time.
(If your battle was quite recent, you could even try rolling back your game a day or two and giving it another go with the above hit numbers in mind.)