I'm documenting how I'm replacing all 16 cords in case I need to do it again, and it might be helpful to others who also need to update their old Kessenich loom, if it's the same. Bruce Niemi, the owner of Kessenich Looms, is very helpful and his advice should be followed though.
Cords
I'm using Oregon #4 1/8" starter cord made in Germany because it's available by the foot from Dickey Bub. I bought 60 feet and used most of it. I used about 30" long pieces for the lower cords and 50"+ for the top cords. It does kink up a bit, so it's helpful to have the old spool to wrap it on.
Replacing Lower Cords
We started with the lower cords which attach to the lamms. Do not make tight knots at the bottom of the lamms because they will probably need to be adjusted after replacing the top cords.
The lower cords are wrapped on my loom about 1 1/2 times when the shaft board is all the way up so you can see the pipes easily and have room to work.
Shafts 1 and 3 wrap toward the front of the loom (lower cords only). Shafts 2 and 4 wrap toward the back of the loom (lower cords only). The wraps for the lamms are closer to the inside of the loom. Shafts 1 and 3 go down in front of the pipe to the lamm; shafts 2 and 4 go down in back to the lamm.
The pipes for each shaft have a large hole and a small hole for both the lower and upper cords. Make a knot near the end of the cord, about 1/2" away, and burn the end to seal it. Feed the cord through the large hole and down into the small hole and pull through, making the knot stay inside the pipe. Take the cord and wrap it the correct direction 1 1/2 wraps (my loom) and then down to the lamm. Tie a knot loosely under the lamm--it will be adjusted later. Do all 8 cords: 4 on each side, to the lamms.
Before tying the knots, make sure to clean and wax the end of the lamms well and into the castle wall.
Shaft 1 pipe has new cord wrapped around it (white/blue cord). You can see the other hole of the pipe where the old upper cord knot is and the old cord that wraps 3 times and goes up to the pulley.
Upper Cords
Cut longer pieces of cord for the upper cords--about 50-60" so you have room to work with it. For each shaft, the upper cord will be wrapped in the opposite direction of the lower cord on the same pipe. This cord goes closer to the castle wall, so wrap so the wraps go toward the castle wall. I used 3 1/2 wraps per cord for my loom. It then goes along the inside of the castle wall up to the pulley. If the cord wraps toward the front, the end goes up the back side of the pipe; if it wraps toward the back, the end goes up the front of the pipe to the pulley. Make sure the shaft boards have the "cut-out" part where the cord will run. We took out all the boards and will wax them and the inside of the castle before replacing them.
You can see the 1st shaft (left pipe) and the 2nd shaft with the new cords in place.
Pulleys
Taking the cord up into the pulley isn't easy. It needs to go up the side of the pulley closest to the outside of the loom and down the other side. We took a thin piece of string or thick thread and fed it down the pulley (the side toward the outside of the loom) until we had a long enough piece to tie to the end of the cord. We pulled on the string and it pulled the cord up the pulley.
Here's the thread ready to pull up the cord.
Then take the cord down the other side of the pulley and down through the shaft board and knot. I am waxing all the boards first and the inside of the castle and will tie loosely until I am ready to adjust all the knots.
From what I understand, when the lamms are up, the shafts will be down, and there shouldn't be a gap larger than 1/2" of the lower shaft hanging down. I really don't want the shaft boards to hit the top of the castle board, though, each time the shaft is raised, so I am going to aim for it to be about 1/4" lower from the top board when raised. I'll consult with Bruce about that, too.
I won't adjust all the knots until I can replace the rubber bumper pads that the shafts will rest on.