An attempt at a brutal summary:
The idea, it would seem, is to keep the number of new elements actually included in any new Turning to an absolute minimum. The three items above are at the top of my list for additions, but there are others which at least deserve consideration
1. Structures and States
So the first point about a possible Fourth (or Fifth) Turning is that, unknown to humans generally, everybody has up to a dozen types of intelligence that appear to have evolved over the centuries to deal with different fundamental issues and problems. These cannot be seen by introspecting or looking within; they are not something we look at, they are something we look through.
And thus any truly comprehensive meditative system would want to be aware of this double development—development occurring in states and development occurring in structures—and thus include both states of consciousness and structures of consciousness in their teachings—the states being how we WAKE UP, and the structures being how we GROW UP. Both, needless to say, are profoundly important.
2. Shadow Work
A few simple psychotherapeutic techniques—such as identifying repressed material, re-owning it, integrating it, then letting it go—would help to handle that nearly 80% of the problems that seem to arise during meditation. But until then, the only advice most meditation teachers have for their students is, "Intensify your efforts!," exactly what is not needed.
3. Meta-theory of Spiritual and Scientific
But whatever meta-theory one adopts, it is clear that any religion of the future will have to have, as part of its dharma, dogma, gospel, or teachings a formal statement on the relation of science and spirituality, and thus a meta-theory of one sort or another would be a likely item in any new Turning.