Thank you @Lex Li (Microsoft) ,
Looking at Azure-VsCode's feature request and issue list, this is not currently supported, and has been deemed as out-of-scope and not planned, unfortunately.
A recommended workaround of using Kudu deployement is advised. Here, a custom deployment directory can be specified in a .deployment file. I wasn't able to get it to work, but maybe others reading this will have more success.