Yes you're correct td, I shouldn't have written it off sooner.
The issue of the TLI window gets covered in some depth in the following..
NASA discussion
Fundamentally if you miss the optimum injection opportunity (i.e. TLI) you will need to perform a plane change as part of the next one, which costs propellant, further away from the optimum slot you get the bigger the plane change/propellant requirement.
The essay actually goes as far as discussing how to generate three TLI windows but ultimately it appears NASA made a decision to go with the "up to three orbits/two injection opportunities" option.
Best guess would then be that decision then drove the requirement for the stage to be capable of orbital cruise of 4.5 hours, for example:
." The [Hydrogen Continuous Vent System] remains in operation for the duration of orbital coast until restart preparations begin. Average duration of coast has been approximately 2.5 hours on Apollo lunar flights although the original design conditions specified 4.5 hours."
University paper
From a battery POV there was certainly enough amps available for several hours post TLI to provide control throughout LM extraction and the subsequent S-IVB slingshot maneuver.
Hope that helps the OP.