There is a possibility to pass Remote-Party-ID through the Sippy Softswitch but such possibility could be activated only via API.
Here are the corresponding methods: http://support.sippysoft.com/solution/articles/3000050243-system-config
An example of usage:
curl -v -k --digest -u <username>:<password> -d '<?xml version="1.0"?> <methodCall> <methodName>getSystemConfig</methodName> <params> <param> <value> <struct> <member> <name>i_customer</name><value><int>1</int></value> </member> <member> <name>key</name><value><string>system/sip/headers/passthrough</string></value> </member> </struct> </value> </param> </params> </methodCall>' https://<environment_ip>/xmlapi/xmlapi
where system/sip/headers/passthrough is a fixed value so you need only to set ssp-root password.
Here is the update method:
curl -v -k --digest -u <username>:<password> -d '<?xml version="1.0"?> <methodCall> <methodName>setSystemConfig</methodName> <params> <param> <value> <struct> <member> <name>i_customer</name><value><int>1</int></value> </member> <member> <name>key</name><value><string>system/sip/headers/passthrough</string></value> </member> <member> <name>value</name><value><string>Remote-Party-ID</string></value> </member> </struct> </value> </param> </params> </methodCall>' https://<environment_ip>/xmlapi/xmlapi