Update a few years later: My answer here may be a cool answer, but this is the correct one. That is how I would solve this problem today.
We could take advantage of the fact that index() almost already does the right thing.
We can’t arbitrarily create instances of various types – we wouldn’t know how to do it, and arbitrary types might not be literal types. But we can create instances of specific types that we know about:
template <typename> struct tag { }; // <== this one IS literal
template <typename T, typename V>
struct get_index;
template <typename T, typename... Ts>
struct get_index<T, std::variant<Ts...>>
: std::integral_constant<size_t, std::variant<tag<Ts>...>(tag<T>()).index()>
{ };
That is, to find the index of B in variant<A, B, C> we construct a variant<tag<A>, tag<B>, tag<C>> with a tag<B> and find its index.
This only works with distinct types.