As far as I can see it's the actual cylinder that is slightly out of spec, not the ammunition.
Lets backtrack a little bit.
Here are the lengths I gave for several brands of 32 S&W Long cartridges.
Sellier & Bellot - 1.265
Fiocchi - 1.270
Remington - 1.260
Mag Tech - 1.270
Those are overall lengths. These are rimmed cartridges. Unless the OP's cylinder is counterbored for the rims, they sit behind the cylinder like in this nice old S&W 32 HE 3rd Model:
The rims on all the cartridges are all right around .050 thick.
Sellier & Bellot 1.265-.050= 1.215
Fiocchi 1.270-.050=1.220
Remington 1.260-.050=1.210
Magtech 1.270-.050=1.220
So if the OP's cylinder is 1.220 long, how is that out of spec?
By the way, the cylinder on my little Smith is 1.250 long. So the bullets of the longest rounds are only sitting back .030 from the front of the cylinder.
The cylinder on this nice little Police Positive .32 is 1.245 long.
As I said earlier, SAAMI Max length of 32 S&W Long is 1.280. So with a SAAMI Max round, the length of the cartridge exclusive of the rim is 1.230. So clearly SAAMI Max length cartridges, or cartridges over Max, would be a problem in that revolver.
I'm sure that revolver was made long before SAAMI existed. Cartridge specifications were looser then, who knows what the industry maximum length would have been. The cartridges are simply too long for the gun, that's all.
32 M&H? I doubt it. 32 S&W Long was a much more common round in those days. 32 S&W? Generally speaking, cylinders for that round were much shorter, like on this old S&W Safety Hammerless. Its cylinder is only .925 long.
No need to go for obscure explanations, it is obvious. The gun is meant for 32 S&W Longs, and the rounds the OP has are a little bit too long.
By the way, lots of old pistols did not have the cartridge specified on them, even very high quality pistols. I have 5 large Top Break Smiths; a Schofield, Russian, New Model Number Three and two Double Action 44s. None of them have the cartridge stamped on the gun.