Asuming that the boat is out of the water, separate the two component nylon stuffing box leaving the aft end attached to the shaft log hose. You didnt mention taking out the original flax packing so maybe you couldnt see it because there is a thin nylon washer over it.

You may have to slice thru the washer with an Xacto knife to remove it and get out the old packing material with a small cork screw type of tool you can get from West Marine. You can replace three successive layers of teflon impregnated packing with the joints spaced as you described. Theoretically, you can do this with the boat in the water and Im sure someone will respond with directions. Assuming this is your first time, Id do it on dry land.

If the boat is in the water, have you first tried just tightening the stuffing box from 1/4 to 1/2 turn? Another quick stop gap measure is to remove only the first layer of packing and install one layer of Teflon flax with Teflon grease.