So after digging around, I found exactly what I'm looking for- a gorgeous squash that stores well- and it's called the Lower Salmon River squash, which is native to the Pacific Northwest and is an endangered plant (information from Renewing America's Food Traditions).
I stumbled upon it at Marishabee's Blog.
This year I grew only one variety of winter squash: Lower Salmon River. I chose this squash because it is fabulous for winter storage. In fact, it will store so well that my partner says that we need a bandsaw to cut through it (we can process it with standard kitchen utensils too).See? That's what I want!
If you're looking for something different to grow, and would like to help preserve and endangered plant, you can buy seeds from Seed Dreams.
Alternatively, if we're neighbors/friends, I might be willing to share some of my stash. But you will be subjected to a growing competition. You've been warned!
Happy garden planning!