The extra serif proves it all as the S has no serif at the bottom on the original strike of the 38 proof. The coin in question you can see that it has been added sort of a second thought. However when you read the write up ,it is discussed that probably the original design did call for an S with serifs on top and bottom,and that when the die was retooled it was added.
You have my attention...LOL. Just did a quick check on the web to see if any of the 1939 Proofs have the extra serif with no luck. One of them could be a rare find or transitional if the "serif" reverse was carried over and used until it failed. IMO, there are some out there and no one has looked.
The reverse of 1940 did have serifs added most notably on the S of pluribus, and on the obverse on the G of God. It wasn't just the step detail that was changed.