Is there a provider and connection string that will allow me to connect to Azure SQL via port 443 the way Access App does? Both SQL Native Client and ODBC seem to only use 1433 which is blocked by my corporate firewall. I'm especially interested in connecting via Excel--possibly with the Power Query add-in.
For that purpose you can try to download this SQL Azure ODBC driver.
All necessary connectivity information you will find on that page.