one option that addresses (a,b) is HDF5  (http://www.hdfgroup.org/HDF5/). the MINC2 (link) format uses HDF5 and is a good option to look into as a starting point.

For those that don't know the NIfTI history I would just like to note that the a critical requirement for NIfTI1 and now NIfTI2 is the agreement to support it from all the major analysis packages. Perhaps in the future they will be prepared to support NIfTI3?=MINC#?, but I believe there is no willingness to do so to date. As a field we seem to be much better off than we were a decade ago, now with NIfTI2 (thanks to Mark Jenkinson and many members of an extended NIfTI Cmte.) and MINC2. If you want the HDF5 advantages for now use MINC2 and I imagine there will shortly be good converters that help deal with the various shortcomings being discussed in this forum.