OP says he's playing the actual schedules. The game log seems to correspond to Retrosheet:
Date # Opponent Result Record Starter Opposing Starter Winner Attendance Time
5- 5-1871 Vs BOS n L 18-20 0-1 Brainard Spalding 5000 2:25
5-13-1871 At CLE n W 12- 8 1-1 Brainard Pratt 1200 2:30
5-15-1871 At KEK n L 6-12 1-2 Brainard Mathews 2:20
5-16-1871 At CHI n L 4-14 1-3 Brainard Zettlein 5000 1:57
5-17-1871 At ROK n W 12-15 *1 2-3 Brainard Fisher 2:15
5-19-1871 At CHI n L 7- 9 2-4 Brainard Zettlein 5000 1:50
5-20-1871 At CLE n W 13- 9 3-4 Brainard Pratt 2:30
5-22-1871 At TRO n W 14- 5 4-4 Brainard McMullin 1000 3:20
5-24-1871 At BOS n T 4- 4 4-4 Brainard Spalding 3000 2:10
5-27-1871 At BOS n W 6- 5 5-4 Brainard Spalding 3000 2:00
I guess the question is whether the historical 1-man rotation was subject to fatigue. We know that most of those pitchers did not throw stuff comparable to modern era pitches. We could either see lower fatigue and lower stuff/movement ratings or assume that teams were willing to go with pitchers who were fairly tired on their third or fourth starts within a week. My guess is that it's somewhere in the middle.