I want to make sure you get the best support for your issue, @fulcher-mark.
The View Archived Forms liability periods only extend back for a year or two. Since you’re unable to find the payroll form you’re looking for, I suggest contacting our live agents to archive it for you.
They can pull up your account in a secure environment and help recreate the forms in your Online Company.
Here’s how you can get in touch with them:
1. Sign in to your QBO account.
2. Go to Help at the top right.
3. Click Contact Us to connect with a live agent.
To ensure that we address your concern on time, you can check out our support hours.
Also, I'm adding ourpayroll tax website it provides articles that will help you prepare your payroll taxes in QuickBooks.
Keep in touch with me here if there's anything else you need. I'll be here to lend a hand. Take good care.