Exchange server delivery issues

I’m getting bounces from Exchange servers, all suggesting that I should contact the administrators to be allowed so send to them, the message listed below. I’m sending from AWS (DMarc 100%, DKIM 100%, SPF 99.97%). I’m not sure where to go from here.

Do I really need to contact my recipients email administrators, and is there an easy way to do that? Are admins likely to respond (we are a legit mailer)?

Your message couldn’t be delivered to the recipient because you don’t have permission to send to it. Ask the recipient’s email admin to add you to the accept list for the recipient. For more information, see DSN 5.7.129 Errors in Exchange Online and Office 365

Have you read this article yet?

This information also applies to error codes 5.7.0 through 5.7.999.

Yes, I have. My read of it is that we don’t have permission to send the recipient. I imagine trying to contact hundreds of mail administrators to get permission to send to their users might be impractical. Has anyone resolved this issue without having done that?

5.7.X issues are policy related. There were multiple issues listed in that Microsoft article. You will very likely need to contact at least one of the recipient domain postmasters. You might start with a phone call to a recipient that is not receiving your email and enlist their assistance in getting you in contact with their Exchange administrator. If your email is being refused in error, someone should be willing to look into the matter.