Definitely an interesting problem. The issue with predictions from predictions is that since the TM makes multiple simultaneous predictions (it predicts unions of possible futures) your SDRs will get denser and denser with each timestep, resulting in less and less precise predictions. However, for any one level of temporal abstraction, maybe that’s exactly what should happen.
In the long run the theory predicts we’ll do this by representing time more and more coarsely at larger scales up the hierarchy. Then at each level you can make predictions at that granularity that get less and less precise as you go multiple timesteps in the future, but you can still predict out to whatever duration you want if you pick a high enough region.
But of course the theory hasn’t yet fleshed out the method of temporal abstraction up the hierarchy (“temporal pooling”). That said, some recent threads on the forum have some promising work in this direction.