When using the Web Reader Adaptor with "Enable Control Port" set to true, only GET and POST HTTP methods are available. The adaptor should allow all supported methods (i.e. matching the list of HTTP methods from the drop-down list).
The only work-around is to have a filter in front with 1 case per HTTP method. For each case, have a Web Reader copy with the default HTTP Method set to the matching case. You need to make sure a map to remove the RequestType field is used before calling the WebReader.