I may be repeating myself but that is quite a worthy project Bikemanbob.
The '501 seamed butted tubing is ever so slightly heavier, and it takes a calibrated butt to tell the difference from '531, IMO.
I am looking at the bar tape and am wondering how to color coordinate with the red and gold accents, unless you find some NOS Benotto translucent gold colored tape. I think I'd end up going with the Newbaums yellow.
PS - Take care when cleaning all those Trek logos - that sprayed-on lettering was not made to withstand much in the way of chemicals.
Bertoni Corsa Mondiale, Bridgestone T-700, Miyata 700 GT, Trek 600, Trek 560 Professional Series, Chrome Panasonic DX 2000, Peugeot PH12, Peugeot PX10, Schwinn World Voyageur, Schwinn Circuit, and Schwinn Voyageur
Here is how the bike looks after I rehapped it. I decided to keep the original freewheel and chain. I would have liked to wrapped the bars in gold tape, but I went with what I had. It will make a great bike for someone.