Well, as my Azure credits will surely run out sometime soon from my MSDN account, I needed to find new hosting. After a lot of searching for the right place, my new home is at TMD Hosting.
I didn’t want a full host to manage, and reading the reviews these are some of the best. The import took a bit longer than anticipated (issues with the Softaculous script), but so far so good!
Next steps are to enable HTTPS via Lets Encrypt.