Given some simplifying assumptions (constant thrust, constant gravitational field, flying in vacuum, over flat horizontal surface), which aren't too badly undermined by the lunar ascent case, the linear tangent steering law is known to give optimal orbital insertion:
$$\tan \theta = A \cdot t + B$$
i.e. the tangent of the thrust pitch angle changes linearly from the point at which insertion guidance starts until circular orbit is achieved. The trouble is that A and B aren't easily derived!
Using a home-brewed simulation using the initial state figures from the Apollo 11 mission report and a very crude, ad-hoc sampling of possible values for A and B, the best-case ∆v-remaining-at-insertion figure I have so far found was for A = -0.002100, B = 0.8040, that is to say:
$$ \theta = \arctan ( { 0.8040 - 0.0021 \cdot t } ) $$
Where $t$ is the time in seconds from when the guidance program takes over. My sim executes a fixed vertical ascent from liftoff until vertical speed reaches 12 m/s, like the actual ascent stage, before switching to this guidance algorithm.
Note that this is the desired thrust angle, thus the commanded vehicle pitch angle rather than the flight path angle $\gamma$ that you asked for, though the two should tend to converge towards the end of the run. If you care about the distinction there's probably some calculus available to derive $\gamma$ from $\theta$, or I could pull the data out of my sim.
The simulator state at insertion and cutoff was a 18.14km x 87.58km orbit, altitude 18.36km, lunacentric velocity 1687.57 m/s, remaining ∆v available 182.18 m/s. Pitch program takes over at T+7.21 seconds and cutoff is at T+436.66 seconds (about 1.5 sec earlier than nominal and about 1.5 sec later than Apollo 11's actual performance). 2218 kg (4889 lbs) of propellant was expended; this compares favorably with the mission planning report, with a nominal ascent requiring 4966 lbs, but it's unclear if the difference is due to unrealistic aspects of my simulation† or an actual improvement in the trajectory. I was unable to find a pitch schedule for the actually-flown ascent; I could make a fair comparison in the sim if I had that.
According to this very thorough guide to the LM descent and ascent programs, the ascent guidance updates on a two-second cycle, which causes the discretization of the pitch observed in the videos.
†: For instance: my simulated vehicle snaps instantly to a commanded attitude, whereas the real LM does not. The real LM ascent engine's nozzle and throat erodes during flight, changing its specific impulse slightly, whereas my sim uses a fixed intermediate value for specific impulse for the whole ascent.
