"I don’t know what it takes to throw the Gargraves, though."
On our train club's modular layout we used some of the prior versions of the Gargraves S gauge switch. We operate them easily with the Tortoise machines and yes it is a must to make the throw arm wire a heavier, stiffer gauge wire as Tom suggested.
The turnout shown in the second post has a throw arm with a hole in it. The other end has a manual throw lever to move the points. I have not used this updated version of turnout yet but the throw arm and throw lever look a lot like the earlier version.If I remember correctly you need to remove the manual throw lever. Use the hole in the right side of the throw arm for the wire from the Tortoise machine.
Compare the earlier version (RH turnout):
with the new version (LH turnout):
It sure looks like they have used the same throw arm in the new switch.
However you do it the Tortoise machine WILL throw the turnout.
I'm guessing the PSX-AR just activates the Tortoise machine.
Mark