So, it turns out that deployment of WordPress in Azure Websites is as easy as one could hope.
Exporting all posts from my previous hosting was simple via the wp_admin page’s Tools/Export plugin (once I deleted all pending comments). Then, I upped the maximum upload file size by adding a .user.ini file to the root of the application via WebMatrix, with the following:
upload_max_filesize = 10M
After that, it was a matter of uploading the rest of the site via FTPS. I’m now interested in moving all media to blob storage, but that can come later.