Does anyone have any ideas that I could improve while still staying in the $2000 price range?
32GB of ram is not super important. You really only need 16GB for gaming, unless you have a buttload of apps going in the background. Personally I would cut the amount of ram down and get a bigger SSD with the budget (or just save the money. Your choice). You could also find a GTX 1080 for a bit cheaper, but Gigabyte is a good company.
I chose the 32gb of ram because I want to be able to stream and also have plenty of applications running while gaming.
Gotcha. The only other thing I would change is get a 1.5/2TB HDD and a 250-ish TB SSD. It'll be a lot faster to have apps that you use frequently (i.e. your OS, steam, and whatever streaming apps you use). It's not all that much more, but it'll be worth it if you use it frequently.