Honestly, thinking more about it, if you're going to do a post VOY Trek show, the only, and I mean only, logical thing to do would be to set it exactly 17 years after the end - not in the far future. This is because the only thing that really makes this era more interesting than other ones in Trek history is you can (for at least the next 20 years or so) still have most of the casts of TNG, DS9, and VOY pop back in as their old characters.
God, no. The last thing I want to see is more scenes of Barclay and Troi saving the heroes of a new show. And you know that's what would end up happening.