680.42(C) will allow the equipment grounding conductor to be un- insulated for that portion that is on the interior of a building for a single family dwelling but the conductors you mention are not supplying the motor and are feeding a remote panel instead making 680.42(C) viod.
This tub is being installed outside.These conductors will be feeders and must comply with680.42 Outdoor Installations.
A spa or hot tub installed outdoors shall comply with the provisions of Parts I and II of this article,As for the ground rods I am at a loss as they are not needed if this tub is680.25 Feeders.
These provisions shall apply to any feeder on the supply side of panelboards supplying branch circuits for pool equipment covered in Part II of this article and on the load side of the service equipment or the source of a separately derived system.
(A) Wiring Methods. Feeders shall be installed in rigid metal conduit, intermediate metal conduit, liquidtight, flexible nonmetallic conduit, or rigid nonmetallic conduit. Electrical metallic tubing shall be permitted where installed on or within a building, and electrical nonmetallic tubing shall be permitted where installed within a building.
(B) Grounding. An equipment grounding conductor shall be installed with the feeder conductors between the grounding terminal of the pool equipment panelboard and the grounding terminal of the applicable service equipment or source of a separately derived system. For other than (1) existing feeders covered in 680.25(A), Exception, or (2) feeders to separate buildings that do not utilize an insulated equipment grounding conductor in accordance with 680.25(B)(2), this equipment grounding conductor shall be insulated.(1) Size. This conductor shall be sized in accordance with 250.122 but not smaller than 12 AWG.
Install the feeders and isolate the grounded (neutral) at the remote panel. Bond the insluated equipment grounding conductor to the enclosure for the remote panel and the equipment grounding conductor of the tub.
With this type of installation the GFCI can be installed at the remote panel. Keep in mind that you are mixing treated water and electricity in the same area that you plan on playing so safety should be in the upper most concern. Making it work is not the answer that you are looking for right now as just because it works does not mean that it is safe.
This tub will also be required to adhere to 680.22(A)(3) also. A receptacle no closer than 10 feet and no farther away than 20 feet will need to be installed. By moving the remote panel away from the tub and installing four conductors the receptacle can be located in the same area and be fed from the same panel.