If I need to, I tell them, "I know it's more, but UPS seems to have issues delivering to this address, so we always ship by USPS."
I have also uses, "My uncle works for the Post Office, so we have to ship it that way to them."
Use whatever you feel comfortable saying.
Generally, I just say, "Priority Mail," if they give me choices. If you say it with authority, as though it was the smartest thing ever said, they rarely question you.
If you are shipping more than 1, less than 2 pounds to Zone 5, the MSC will adjust the reimbursement.