I do pretty much the same thing, except I use clear plastic aquarium tubing to snake down through an empty egg space in the turner and inject water through it with a 60 ml/cc syringe. If adding more than one syringe of water, I usually warm the water slightly in the microwave to take the chill off before adding to the incubator.
I also use the aquarium tubing/syringe injection method to get water onto sponges in the incubator during the last few days of hatching.
Either tubing or a straw get the job done - whatever fits the tip of any large syringe that you can find.
I have a 9200 that I use as a hatcher, but if I had the turner in it, I would probably install some aquarium tubing through the wire grate and up through the turner and out a vent hole before getting started with each incubation run. Then put something around the tubing at the vent hole to seal it to keep the humidity and heat in. Crimp the end of the tubing with a gem clip to keep it closed when not adding water. That way there would be a tube installed during the whole hatch through which water could be added as needed. If done this way, I'd recommend disposing of the old tubing and installing new tubing with each hatch.