Hi Dick, I hope I'm correct here. But why would Brophy put it in his book that the 5,000 carbines built in 1898 and were built on 1898 actions, and then Brophy states all of the info for the carbines using the model 1898 actions which shows that 29,000 were made using model 1898 actions per Brophy. He broke it down as  follows, Model 1898 carbine 5,000 with the model 1898 action, then the model 1898 converted carbine for 3,000. Then the M1899 second model built using 16,000 model 1898 action. Add that up and that is a total of 29,000 carbines built or converted for use. Brophy did a great job showing which action was used for which build. He says the M1899 carbine first model  was built using 9,000 model 1896 actions. And that the M1899 second model was built with 16,000 model 1898 actions. And that the M1899 third model was built using 2,000 model 1901 actions. So just in the model 1899 carbine series they used 3 different action, the model 1898 for 16,000, then 9,000 using a 1896 action and then 2,000 for the model 1901 action. That totals up to 27,000 of these M1899 carbines.
If everyone is reading the same info from Brophy and sticking to that 5,000 model 1898 carbines made using 5,000 model 1898 actions then you can't dismiss the rest of these, they are Brophy's figures and accounting. This is the info I pulled from Springfield armory and Brophys book.
Mike