I am not sure you will find any more in print than what you already have, Richard. Nothing I know of at least. My understanding is that the C- prefix serial numbers designate commercial mfg from Colt's, as distinguished from U.S. military contract. I believe all the production for other countries are going to have that C- in the serial, though there may be exceptions. Those were considered commercial sales. The Colt's sales ledger in Dolf's Vol I shows sales to specific countries as well as to various aircraft makers who were also supplying product overseas.
Colt's seems to have updated the model name of the water cooled guns a number of times from the post-WWI period and into the 1930s. From what I have observed, MG38 water cooled guns were, at first, almost identical to what we know as the Argentine contract 1928s. I believe the Argentines contracted was merely the standard commercial Colt gun of the period, with perhaps minor differences for their specific needs. Caliber being one, of course, and it may be the rear sight graduations were caliber specific. But the general form of the rear sight I have seen on MG38s is much the same as the 1928s. At some point, a heavier water jacket was introduced. To go with that, there was a water circulation pump system, similar to what the .50 cal M2 guns had in U.S. service. I don't know what years the model names changed and such features were added. The MG38B version may have designated new features, but I don't know for certain.
First commercial model I know of was marked the 1919 water cooled, looking indistinguishable from the WWI U.S. 1917. The next variation I am aware of was the 1924. At some point, the new construction of the bottom plate came in, such as we see by the Argentine contract guns. I believe that remained the standard on commercial water cooled guns into WWII. I am not aware of any Colt manufactured guns with the WWII style bottom plates, except those converted by the Ordnance Dept from WWI stocks.
One other difference I have seen on some MG38s is that the Elevating Bracket is riveted to the bottom plate, rather than mounted by 4 screws as on the 1917s and 1928s. Another feature added at some point was the top latch with a "trigger" shaped lever that lifts the leaf spring for ease of operating the latch. It might be that old Colt's catalogs would be the best source to date the changes and revisions, if a range of years could be found to study. I don't think any books have covered the MG38 in depth, so we go by examples seen as much as anything else. There was a spade grip assembly made for these as well, and they are not very common. That would have required a unique trigger, I think. However, the major internal parts on these do not vary that much. I believe that the specs in place by the 1928 Argentine contract all included the captive drive spring, so that bolts would be specific to that feature from that point forward, distinguishing them from military bolts.
Also worth mentioning is a series of air cooled models that were intended for tanks I believe. I think these show up in the East Indies. I know of one in Australia, so they may have been sold to commonwealth forces for that region against the Japanese. These are shown in Dolf Vol I as well, and I think they were the MG38T and MG38BT, the distinction being one had the spade grips added. Key to this model is a very different receiver construction, with more rivets in the top and bottom plate assembly. Also, they have a trunnion mount adapter similar to aircraft Brownings. This same receiver was adopted by Uncle Sam only as the 1919 Aircraft gun, in about the mid 1920s, and did not serve long in our military. I've seen two examples of that, with the same receiver Colt sold as the MG38T/BT in air cooled config. Hope there is something useful here.