I'm going to have to give this some thought but my gut feeling is once you've launched into what is effectively an inertially referenced earth orbit I'm not sure a "TLI window", driven by celestial mechanics comes into it, at least not for a few hours - every orbit you should come back around to the roughly same fixed point in space where TLI needs to start but of course that's not fixed relative to the ground.....(and I'll stop digging a hole for myself at that point). I've seen reference somewhere (I'll have to look it out) to early work on the S-IVB and a TLI as late as six hours/three orbits plus was investigated - as I recall, and I'm hazy on this, it that was possible from a guidance /S-IVB consumables standpoint but was suboptimal in other areas, including the possibility it would have placed a definite requirement for a larger than ideal initial course correction using the Service Propulsion System.
As you say LH2 loss and battery life will have been the bigger player, the early declared spec for the S-IVB ended up being four to five hours in orbit prior to TLI, which fits with the usual plan of TLI after e.g. 2 hours 45 min GET (Apollo 11), and for them the second and final option at 4 hrs 15min...
Have you had a dig around techy sites using google such as e.g. the Apollo experience reports?
FWIW
NASA stuff