can't get flax stuffing into gland nut

I cannot believe the difficulty I am having at getting new stuffing into my port shaft. Through all I have researched and measuring that I have done an 1 3/8 shaft calls for 5/16 packing. It just won't go into the gland nut. I have even tried to squash by hitting it with a hammer before wrapping it around shaft. Pieces of the old that I dug out appear to be 5/16 but the new just won,t go in. The parts man at my local supplier said I could probably get by using 1/4 flax and adding an additional ring of flax having 4 vs 3 rings. Anyone have any thoughts about doing that or any other any other recommendations on getting this to work. Thanks