Welcome to the QuickBooks Community, kctwarrior. You're right that the QuickBooks system only requires entering tax rates between .7% - 5.4% when setting up Oregon State tax information. Let me route you to our support to assist you further.
Since Oregon only requires the rate mentioned, I recommend contacting our QuickBooks Online Team. They have the tools to check your account in a secure environment and change SUI as tax-exempt and set up this on your end.
Lastly, you may refer to this article if you want to view your employee's info, wages, taxes, and deductions: Run payroll reports.
You're always welcome to post if you have any other concerns about setting up and managing SUI in QuickBooks. I'm always around to help, kctwarrior. Have a great day!