Was dreading the day my laces were inevitably going to break and it finally happened. Took a couple of hours but after some trial and error, I think the best way is to cut an end of the factory laces and remove part of the core. Then push the new lace (remove any plastic caps) into where the core is and use sewing thread and a whipping knot to connect them. Make sure to wrap it very securely so it doesn't pull out. Once the new lace and old lace are connected I was able to pull hard enough to just feed the new lace in as I pull the old lace out. This was able to get it in the most forward eyelets which are impossible to reach without infant hands.
I had to do a lace replacement on Phantom techs last year and was somehow able to do by hand, but remember it being very tedious threading through the first eyelets. Your pull through method is clever, saves some frustration, and looks like a much better technique.