Curiously, the 29C and 19C hold the X register in continuous memory but not the Y, Z, T nor LASTX registers. I wonder why they didn't go for the whole shebang? Or why they didn't even bother holding the X register in the Spice "C" machines.
My guess is that all the stack registers in the Woodstocks are on the CPU (ACT) chip. But in the 29C and 19C they keep a copy of it in the CMOS chip as well. (Probably this was a design compromise between CMOS storage space cost and wanting to keep the whole stack in CMOS.) Upon power-up they copy back from the CMOS chip. In the Spice machines they went for low cost and consistency of design so gave up on this idea.