Hi -
I've also got that watch, albeit on the classic khaki band.
However, it's not an A-11. The movement inside is a Elgin 685, the original Elgin A-11 has an Elgin 539 with 16 jewels (this according to the TM 9-1575 War Department Technical Manual: Ordinance Maintenance, Wrist Watches, Pocket Watches, Stop Watches and Clocks from 6 April 1945, War Department, i.e. the repair manual for military watchmakers...). The movement in the A-11 is actually the Model 1783 Grade 539, 8/0 size.
You've probably got engraving on the back showing it as an A-11. The case is fine, just that someone, somewhere, has a bunch of NOS Elgin 685 movements from gun cameras from the Korean war and NOS A-11 cases, and put the cases and the movements, along with the dials, together. I got mine on eBay, and I call it my A11Franken. We've had a discussion on this over on vintages a while ago, and I am convinced - it took some convincing, too - that this is, unfortunately, not a real issued watch.
It's an outstanding movement: 18 jewels, 18'000 beat, 23.7mm diameter, 8/0 size, and was adjusted for multiple positions. It was manufactured in both 12 and 24 hour variants, and was probably one of the finer Elgin movements made for the military. I know mine shows excellent isochronism and runs around 7s/day fast, which given the age is righteous indeed.
But the production run was in 1952, according to Ranfft.
JohnF