On second thought, since I assume the generator and its battery are subject to significant outdoor temperature variations, you should consider temperature compensation of the charging voltage.
This from the Battery University website:
"Heat is the worst enemy of batteries, including lead acid. Adding temperature compensation on a lead acid charger to adjust for temperature variations is said to prolong battery life by up to 15 percent. The recommended compensation is a 3mV drop per cell for every degree Celsius rise in temperature. If the float voltage is set to 2.30V/cell at 25°C (77°F), the voltage should read 2.27V/cell at 35°C (95°F). Going colder, the voltage should be 2.33V/cell at 15°C (59°F). These 10°C adjustments represent 30mV change."
Below is the LTspice sim of an LM317 circuit to do that.
It uses a TL431 programmable reference to control the output voltage, along with two diodes, whose forward voltage drop change with temperature generates the desired -18mV/°C output voltage change.
The LM317 here is only used essentially as a "smart" transistor with current limiting and over-temperature protection, since the TL431 controls the LM317 ADJ pin voltage to regulate the output voltage.
Resistor Rlim determines the charge-current limit, so a separate LM317 for that isn't required.
D3 protects the LM317 if the battery is connected without charger power.
Trimpot U3 allows adjustment of the float voltage, which is typically set to 13.5-13.8V @ 25°C.
The sim below shows a -383mV change in output voltage for a 20°C rise in temperature, reasonably close to the desired 360mV (60mV/cell).