Basics for Towing
It doesn't seem to me that anyone has done anything except tell you about things they have seen or done years ago.
I have been towing everything from tow dolly's to 3 car haulers since the 70's.
The very first thing you should consider is the hitch. Your basic light duty hitch, 2500 lbs and under, can be bolted or welded to the rear frame rails or through the trunk floor pan with a steel reinforcement on the inside of the pan. If you are going to bolt to the bumper in anyway, I suggest welding the bumper brackets at the frame and reinforcing behind the area the bracket bolts to the bumper. I will admit after re-reading your original post not all of this may be necessary for 800 lbs. Although are you sure you won't find another 600 lbs or so in coolers, clothers, etc, etc.
Any transmission used to tow for this distance should have an external cooler. Your PG is probably cooled through the radiator, therefore the hotter the motor gets, the hotter the trans fluid will get.
Check the ratio of your rearend. I would not try to tow anything without at least a 3:08 ring & pinion. The optimum gear would be a 3:36 with the PG.
Lastly the brakes. Although the 67 has upgraded brakes from the 1st gen's, they still will fade with repeated usage on downgrades and in the heat of summer. The disadvantage of the PG is you can't really help yourself slow down by downshifting. At least with a 350 turbo, you can downshift to 2nd gear to help control your speed on the downhill. Using the brakes on an extended down grade will not only heat them, causing fade, but there is always the possibility of the no-brake trailer trying to pass you.
The suggestions above are based on the fact you are planning an extended trip. We used to use all kinds of rigs just to get to the track on a Sat. night. The wear and tear of 5000 miles will requirer more than a hitch and lights.
By the way, I have driven and towed Rt 66 from IL to CA several times and although it is not as tough as the I-70 Vail Pass in CO or I-90 in WA & ID, it has a fair amount of elevation changes that will challenge your 67.
