I count 365 as well. I don't know how I didn't forsee this. I had thought when I finalized the all-timer lists that I had given us enough players for a full 25 rounds. Don't know where I screwed up, but it looks like we're going to be 35 players short.
Here's what I propose to do. Here is a list of 37 200K players from between 1885-1900. We'll use these players to fill out our rosters. These are one year players only, none of them can be included on any keeper lists for 1902.
1891 Bob Barr P
1887 Bill Bishop P
1889 Davey Dunkle P
1899 Jim Gardner P
1889 Bill Garfield P
1894 George Haddock P
1889 Ed Knouff P
1890 Gus Krock P
1899 Al Maul P
1899 Harry Moupin P
1894 Charlie Petty P
1888 Dupee Shaw P
1900 Tom Thomas P
1899 Harry Wilhelm P
1888 Tug Arundel C
1892 Grant Briggs C
1885 Cal Broughton C
1891 Buster Burrell C
1889 Bart Cantz C
1891 Bob Clark C
1892 Bill Moran C
1886 Dave Oldfield C
1896 Dave Zearfoss C
1894 Willard Brown 1B
1890 Pat Hartnet 1B
1890 John Kerrins 1B
1895 Harry Spies 1B
1890 Dad Little 2B
1892 Jimmy Knowles 3B
1899 Frank Martin 3B
1892 Harry Raymond 3B
1885 Billy Greer SS
1885 Jim Halpin SS
1899 Scott Hardesty SS
1888 Red Ehret OF
1892 Buster Hoover OF
1896 Tom Niland OF
We can distribute them by continuing on with the draft with these players once all of the regular players have been selected, or we could simply randomly distribute them, 2-3 per team. No one here is going to play much if at all, research is pointless since they're all terrible anyway. Let me know which method you would prefer.
This also brings up the issue of AAA. Since I miscounted the players, particularly pitchers, we will set it up so every team gets two "average" AAA pitchers and two "average" AAA position players, who can be called up and used as well as traded. Ideally, I'd like for this league to have zero "fake" AAA players, and hopefully we won't have to use them for more than a season or two as our available players increase.