"There's no way anything would turn up this close to the town at this point."
Depends entirely on where the dragon was. Being close and convenient to the town just means it's going to be found faster, not whether it will be there at all.
"We've got no choice but to search every which way at random."
Nah, you can search in more efficient patterns. And you can just choose not to.
In fiction, powerful monsters are drawn to each other. In reality, animals like that tend to avoid each other. Conflict is generally a bad idea.
It's always the quiet ones... Well, science people tend to get excited when there's something new to test.
Not sure getting greedy would apply as much in an area that isn't that dangerous. It's usually more about getting greedy in dungeons or other actually dangerous places.
Of course it's an expensive ring. Why wouldn't it be?