Incremental backup split across files
Absolutely, that is an option. Do the full backup, and then log backups. At the receiving end, restore all but the last using NORECOVERY. 

Automating regular log backups and then restoring at the other end is what we call "log shipping", and there's a feature to do that using Agent jobs in SQL Server. Might, or might now, be relevant for you depending on your setup. Possibly not because of your cloud environment (it uses a share to store the backup files, which the originating server needs access to.

Whether to then stripe one backup over several files (not sure if you had this in mind), depends on whether it is beneficial to have several files for the transfer process. I doubt you gain much with striping for the log backups.