That's why it likely was 9x40 Armco. Basically a short 357 Sig but loaded to much higher pressures. It was developed to use cheap 40S&W brass instead of 38 Super in IPSC race guns.Making .357 brass isn't as easy as just running .40 through a die. The case will be .020" too short. You may get misfires and accuracy will suffer too. I doubt it works the other way.
I've resized it back to 40S&W and the occasional case does split. Problem is it may have a bump when resized and may fail to chamber. Looser chambers like my S&W M&P would work most of the time.i am told that the case cracks when you try to resize it to 40.