We towed our 4,000# camper to Glacier and back this summer. I've also towed my compact tractor (about 5,800#) around here, and my buddy uses his GX460 to tow his 5,000# boat. So, yeah they'll tow just fine up to the 6,500# rating.
The LX570/LC200 used the same A760F your GX has until 2016 I think when they went to the 8 speed. As did all years of the 2nd gen Tundra (which are rated to tow far more than a GX460 is). The LX570/LC200 also have a UR engine that has the starter in a difficult spot, and there are reports of them having valley plate leaks like the 460 too. Other than beefier diffs, I don't see how they'd be any more reliable mechanically than a 460 is.
If you want to avoid the A760F, you need to get a 100 series or a GX470

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