Using Apple Pay and Hide My Email

Today I purchased an umbrella from Shady Umbrella Company (SUC) on my Mac and opted to use Apple Pay. Before confirming the transaction on my iPhone or Apple Watch, a screen pops up with shipping and contact information. This information is obviously necessary for SUC to ship the umbrella and notify me when it is on its way. Unfortunately, the contact information would not accept or give me the option to use a Hide My Email (HME) or an alias email - an HME greatly preferred. To complete the transaction, Apple Pay would only accept my iCloud root email address, which is then given to SUC. THIS DEFEATS THE WHOLE PURPOSE OF HME.

Interestingly, had I done the transaction with PayPal, SUC would have been given an HME.

Does anyone know a work around for this problem using Apple Pay or should I just use PayPal and not Apple Pay?