We just did this for a new car. Also have USAA and bought cars through their car buying program previously, but they discontinued it.
2 werks ago, spouse negotiated with dealership and negotiated xx price. Entered the info into the online Costco car buying program, and it saved us $3k for the SAME CAR.
Super simple, people were great to work with, and that's $3k that can go towards to 2 college payments this fall