Old Fuff
A couple of things come to mind; in 1906, did Colt ask Mr. Browning to come up with a more powerful round for the Model 1903, and that in collaboration with William Thomas of UMC/Remington Arms, design such a cartridge, the result being the .380 ACP? And didn't Mr. Browning then spend the next two years modifying the Model 1903 to function with the new round, eventually resulting in the Model 1908? If this were so, then wouldn't it explain the different measurements and dimensions which would make interchangeability between the two models somewhat questionable. As you pointed out, Colt ran the Model 1908 with its own run of serial numbers; if it were just another caliber addition (as was common with their revolvers), then why didn't they run the serial numbers in with the Model 1903 production? It would seem that in early production, at least, the Model 1908 was a dimensionally different gun than the Model 1903.
There was also a story I heard about the .380s that the Shanghai Police used during the time you mentioned. It had something to do with a cut-out made on the magazines that were issued to the police officers. It seemed that some of the officers had a penchant for selling their issued ammunition on the black market. They would then replace those rounds with some dummy ones as to give the appearance that the magazine was still fully loaded whenever weapons inspection came around. Eventually the higher ups caught on to this "practice" and had the magazines modified so that the primers could be seen through the cut-out slot in the back of the magazine. I have no idea if this is true or not. Just a story I heard (and I saw a magazine so modified, but couldn't verify by whom, or when).