Maybe I am wrong but I think adding a variable into the field “Contact User” in the trunk settings is not supported. I think the only way you can do that is by writing a custom dialplan for the [macro-dialout-trunk-predial-hook] context in the extensions_custom.conf file.
[UPDATE]
There is an option “Caller ID into Contact Header” in the GUI (see the post below). I think this is the solution you are looking for.