Phil,
I’m going to list the routes I believe the teams would have used. I would guess the travel times would not be too much slower than Amtrak’s. Mileage approximate.
All 16 teams would not use the same routes, I have only listed my best guesses.
1-Boston to New York (AL and NL)
New York, New Haven and Hartford 230 miles.
2-New York and Philadelphia(AL and NL)
Pennsylvania RR 90 miles
3-Boston and Philadelphia (AL and NL)
combine the first two routes with a cross town transfer in Manhattan
4-Philadelphia and Washington (AL)
Pennsylvania RR 133 miles
5-New York and Washington (AL)
Pennsylvania RR 224 miles
6-Boston and Washington (AL)
B-NY + NY-Wa + transfer
7-Philadelphia and Pittsburg(h) (NL)
Pennsylvania RR 348 miles
8-New York and Pittsburg(h) (NL)
Pennsylvania RR 438 miles
9-Boston and Pittsburg(h) (NL)
B-NY + NY-Pi + transfer
10-Pittsburg(h) and Cincinnati (NL)
Pennsylvania RR 310 miles
(B&O 15 miles longer, both through Columbus)
11-Philadelphia and Cincinnati (NL)
Pennsylvania RR 658 miles
12-New York and Cincinnati (NL)
Pennsylvania RR 748 miles
13-Boston and Cincinnati (NL)
B-NY + NY-Ci + transfer
14-Cincinnati and St. Louis (NL)
Baltimore and Ohio 338 miles
15-Pittsburg(h) and St. Louis (NL)
Pennsylvania RR 611 miles
16-Philadelphia and St. Louis (AL and NL)
Pennsylvania RR 959 miles
17-New York and St. Louis (AL and NL)
Pennsylvania RR 1,050 miles
18-Boston and St. Louis (AL and NL)
New York Central system 1,200 miles
Boston and Albany to Albany 200 miles
New York Central to Cleveland 476 miles
Cleveland Cincinnati Chicago and St. Louis to St. Louis 524 miles
19-Washington and St. Louis (AL)
Baltimore and Ohio