Interesting. The output voltage can be increased by increasing the current going through the rotor, which can be done by increasing the rotor voltage, and probably modifying the voltage regulator (which controls the rotor current). The stator should be fine because, when delivering power at a higher voltage, the output currents will be lower. That current is the main heat source...
Voltage can also be increased by increasing RPMs, but I assume the 3600 RPMs are a given constraint.
The alternator must have a current limiter, because the load presented by the motors can be abnormally high when they get stuck due to obstacles, etc. A fuse would be a pain, unless it is a solid state fuse of sorts.
The idea of putting two alternators in series is clever, and solves the issue of heat dissipation, as each alternator would be air cooled separately even if the share the same axle.
On a separate tangent I thought that gas powered lawn mowers will be soon banned, so perhaps explore a small green hydrogen fuel cell, power the motors, and produce clean water to irrigate whatever you were mowing. I visited this week the friend that is prototyping a 1MW Data Center in Mountain View on green hydrogen, off the grid. I am a convert. Great stuff, I can post a picture. Goes live in a few weeks. That IS the future.