It seems you are right, PUT is not supported.

Maybe you could use the CONNECT method instead and let the client talk directly to the FTP server.

Something as drawn in the following diagram:

 .---------------.               .------------------.
 | FTP Client    |               | Apache Listening |            .----
+------.
 | with HTTPS    |---------------| for SSL          |            | FTP
+      |
 | over SSL      |    SSL conn.  |                  |            | Ser
+ver   |
 | Proxy support |-------------------.           .---------------.    
+      |
 |               |       FTP conn    |<-CONNECT->|    FTP conn.  |    
+      |
 |               |-------------------'           '---------------'    
+      |
 |               |               |                  |            |    
+      |
 |               |---------------|                  |            |    
+      |
 |               |               |                  |            '----
+------'
 '---------------'               '------------------'
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