This is from distant memory, for I sold the boat with a WC Imperial head
ten years ago (I believe that the piston rod packing is similar).
I too found that if I tried to install the entire new packing that the nut would not engage... so I cut the packing in half with a razor blade, installed the smaller piece and tightened the nut down. Then removed the nut and added the other half and found that the nut would then engage. IIRC it worked fine after that.
One other thing I did to improve the system was to discard the leather cup seal on the piston and made up a new piston that incorporated a fairly fat o-ring instead of the leather. Worked way better, and lasted essentially forever, whereas the leathers wore out in a year or so of constant use.
Good luck, and good flushing!