The chassis on my 612 is beginning to make sense now....It has lots of empty holes where I now see tube on the 571.

5 25Z6 tubes in series would give you 125V heater string. So I'd expect that to go directly across the powerline, and not the top of the autoformer winding, as in the diagram. Unless the autoformer was only boosting the line voltage say 10V. Or is it an error Sams' made?
http://antiqueradio.org/art/temp/FiveRectifierTubes.jpg