Here is some more information that I have had a chance to look up, this is out off Brophy's book.
M1898 carbine 5,000 made using model 1898 actions.
M1898 converted carbine 3,000 made using the model 1898 action.

M1899 carbine first model made using model 1896 actions, 9,000 made.

M1899 Carbine second model made using model 1898 actions, 16,000 made.
M1899 Carbine third model made using Model 1899 actions, 2000 made.
If I'm reading the prodution correctly they used what ever they had and built them in lots, with 3 or 4 distinct seperate models of carbines produced using these model 1898 actions. They were even used up until 1905 for some rifles.
Mike