C++ method method with multiple parameter packs

Consider the following simplified piece of code for a variant class. Most of it is for informational purposes, the question is about the conditional_invoke method.

// Possible types in variant.
enum class  variant_type { empty, int32, string };

// Actual data store.
union variant_data { 
    std::int32_t val_int32;
    std::string val_string;
    inline variant_data(void) { /* Leave uninitialised */ }
    inline ~variant_data(void) { /* Let variant do clean up. */ }
};

// Type traits which allow inferring which type to use (these are actually generated by a macro).
template<variant_type T> struct variant_type_traits { };
template<class T> struct variant_reverse_traits { };

template<> struct variant_type_traits<variant_type::int32> {
    typedef std::int32_t type;
    inline static type *get(variant_data& d) { return &d.val_int32; }
};

template<> struct variant_reverse_traits<std::int32_t> {
    static const variant_type type = variant_type::int32;
    inline static std::int32_t *get(variant_data& d) { return &d.val_int32; }
};

template<> struct variant_type_traits<variant_type::string> {
    typedef std::string type;
    inline static type *get(variant_data& d) { return &d.val_string; }
};

template<> struct variant_reverse_traits<std::string> {
    static const variant_type type = variant_type::string;
    inline static std::string *get(variant_data& d) { return &d.val_string; }
};

// The actual variant class.
class variant {
    public:

    inline variant(void) : type(variant_type::empty) { }

    inline ~variant(void) {
        this->conditional_invoke<destruct>();
    }

    template<class T> inline variant(const T value) : type(variant_type::empty) {
        this->set<T>(value);
    }

    template<class T> void set(const T& value) {
        this->conditional_invoke<destruct>();
        std::cout << "Calling data constructor ..." << std::endl;
        ::new (variant_reverse_traits<T>::get(this->data)) T(value);
        this->type = variant_reverse_traits<T>::type;
    }

    variant_data data;
    variant_type type;

    private:

    template<variant_type T> struct destruct {
        typedef typename variant_type_traits<T>::type type;
        static void invoke(type& v) {
            std::cout << "Calling data destructor ..." << std::endl;
            v.~type(); 
        }
    };

    template<template<variant_type> class F, class... P>
        inline void conditional_invoke(P&&... params) {
        this->conditional_invoke0<F, variant_type::int32, variant_type::string, P...>(std::forward<P>(params)...);
    }

    template<template<variant_type> class F, variant_type T, variant_type... U, class... P>
        void conditional_invoke0(P&&... params) {
        if (this->type == T) {
            F<T>::invoke(*variant_type_traits<T>::get(this->data), std::forward<P>(params)...);
        }
        this->conditional_invoke0<F, U..., P...>(std::forward<P>(params)...);
    }

    template<template<variant_type> class F, class... P>
        inline void conditional_invoke0(P&&... params) { }

};

The code works this way, i.e. it works as long as the parameter list P... for the functor is empty. If I add another functor like

template<variant_type T> struct print {
    typedef typename variant_type_traits<T>::type type;
    static void invoke(type& v, std::ostream& stream) {
        stream << v;
    }
};

and try to invoke it

friend inline std::ostream& operator <<(std::ostream& lhs, variant& rhs) {
    rhs.conditional_invoke<print>(lhs);
    return lhs;
}

the compiler VS 20115 complains

error C2672: 'variant::conditional_invoke0': no matching overloaded function found

or gcc respectively

error: no matching function for call to 'variant::conditional_invoke0 >&>(std::basic_ostream&)'

I guess the compiler cannot decide when U... ends and when P... starts. Is there any way to work around the issue?