Thanks OldGriz, I knew I had to be coming. But if your Sheaffers ever change their mind . . .
Philm, here is my Big Red:


And here are my biggest and smallest pens together:

The imprint is fairly worn away, but reads: "Geo.S.Parker Parker Duofold Made In U.S.A.". The nib reads "Parker Duofold Pen P". It doesn's say "Lucky Curve" anywhere on it.
All I can tell is that this is a later version -- after 1928 when the cap band split and as late as 1931 according to the imprint dating in acfrery's portugese document. It seems to be in good shape to my limited experience and writes very well. Compared to my other vintage pens, this has a much stiffer nib, yet smooth, which I enjoy switching to from time-to-time. Also despite its size, it has proven to be very comfortable for extended writing. Currently I have Private Reserve Orange Crush loaded in it, but it's a little too close to the color of the pen and for some reason bothers me; almost like the pen is bleeding when I write with it.
Thanks again for your help!
Best,
Rich