+1 on the water bath. Get a rubbermaid container, put the turkey in it and let it soak in ice water for a few hours to pull excess salt out. Repeat if needed. Then prop the bird up and let it drip dry, help it along in the interior with a few paper towels.

Also +1 on eliminating the salt completely from your rub.

If you can, mix some of the rub with a bit of butter and insert it between the skin and the meat in the breast area. This helps the turkey absorb more flavour. Also put the rub inside the bird if you are not stuffing it.

Alternatively, if possible, convert your recipe into corned version? Same soak as above in ice but brew your spices and soak-marinate in saltless spice mixture. Cook under foil and crisp the skin with a culinary torch prior to serving.