In the answers to your previous post, there were a couple of people, me included, that recommended using const_iterators instead for non-performance related reasons. Readability, traceability from the design board to the code... Using const_iterators to provide mutating access to a non-const element is much worse than never using const_iterators at all. You are converting your code into something that only you will understand, with a worse design and a real maintainability pain. Using const just to cast it away is much worse than not using const at all.
If you are sure you want it, the good/bad part of C++ is that you can always get enough rope to hang yourself. If your intention is using const_iterator for performance issues, you should really rethink it, but if you still want to shoot your foot off... well C++ can provide your weapon of choice.
First, the simplest: if your operations take the arguments as const (even if internally apply const_cast) I believe it should work directly in most implementations (even if it is probably undefined behavior).
If you cannot change the functors, then you could tackle the problem from either side: provide a non-const iterator wrapper around the const iterators, or else provide a const functor wrapper around the non-const functors.
Iterator façade, the long road:
template <typename T>
struct remove_const
{
    typedef T type;
};
template <typename T>
struct remove_const<const T>
{
    typedef T type;
};
template <typename T>
class unconst_iterator_type
{
    public:
        typedef std::forward_iterator_tag iterator_category;
        typedef typename remove_const<
                typename std::iterator_traits<T>::value_type
            >::type value_type;
        typedef value_type* pointer;
        typedef value_type& reference;
        unconst_iterator_type( T it )
            : it_( it ) {} // allow implicit conversions
        unconst_iterator_type& operator++() {
            ++it_;
            return *this;
        }
        value_type& operator*() {
            return const_cast<value_type&>( *it_ );
        }
        pointer operator->() {
            return const_cast<pointer>( &(*it_) );
        }
        friend bool operator==( unconst_iterator_type<T> const & lhs,
                unconst_iterator_type<T> const & rhs )
        {
            return lhs.it_ == rhs.it_;
        }
        friend bool operator!=( unconst_iterator_type<T> const & lhs,
                unconst_iterator_type<T> const & rhs )
        {
            return !( lhs == rhs );
        }
    private:
        T it_;  // internal (const) iterator
};