Because of the missing parens on the proxy call you're attempting to call METHODNAME on something thats an unblessed reference (namely the vanilla arrayref you're trying to pass proxy).

(
    (
        my $soap_response =
          'SOAP::Lite'
          ->new->service('file:FILE.WSDL')->uri('http://URI.URL')->pro
+xy
    ),
    [ 'HTTPS Proxy URL', 'credentials', [ '$username', '$password' ] ]
    ->METHODNAME($post)->METHODNAME('string')
);
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perl -MO=Deparse,-p,-q is your friend.