Can I convert a reverse iterator to a forward iterator?

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Reverse iterators have a member base() which returns a corresponding forward iterator. Beware that this isn’t an iterator that refers to the same object – it actually refers to the next object in the sequence. This is so that rbegin() corresponds with end() and rend() corresponds with begin().

So if you want to return an iterator, then you would do something like

std::deque<Move>::const_iterator Current() const
{
    if (forward)
        return currentfwd;
    else
        return (currentbck+1).base();
}

I would prefer to return a reference, though, and encapsulate all the iteration details inside the class.

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