There is no 4K die. The 4K chips are using 8K dies, the lattice software limits the number of usable LUTs to 4K. IceStorm will give you access to all 8K LUTs in the device.
Really? On the http://www.clifford.at/icestorm/ IceStorm site - If you look carefully at the table of supported devices - the ICE40HX4K-144 is there - 2 rows from the bottom
Am I right in thinking 8K refers to the number of LUTs/cells? If so I won't be fitting the Rocket RISC-V design in one any time soon. Although it's a good start - I'll be very happy to see the back of Xilinx Vivado awfulness one day.