You happen to be dealing with a time period where extrapolation from known lettered ship dates is less reliable than at other times.

The Great Depression slowed sales dramatically. Just looking at the serial ranges, comparing 1919 to 1929 with 1929 to 1939, sales of M&Ps crashed by 75%, from over 300,000 to around 75,000. This led to considerably more out-of-sequence shipments and delayed shipping than usual. Guns sat in the safe longer and were more prone to be picked out of sequence than at times when guns flew out the door.

So if you want any more certainty than you already have, a letter or joining SWCA are really the best ways.