The widely used rule is to use the Laplace sphere rather than the Hill sphere, which is what you are using.
I sicced an intern on a rather related problem a decade ago, which was to find the best place to switch the frame of reference in which gravitation is computed in a simulation that integrates the equations of motion.
I had him use an arbitrary precision arithmetic package to develop reference trajectories for a vehicle on an outbound trans-lunar trajectory and an inbound trans-earth trajectory, using a variety of integration techniques. I had him calculate two reference trajectories for each leg, one Earth-centered inertial and the other Moon-centered inertia. The goal here was to get consensus reference trajectories that agreed to over 20 decimal places of accuracy.
Then I had him use standard IEEE double precision numbers for the integration, switching frames of reference when the vehicle became closer than (trans-lunar trajectory) / further than (trans-earth trajectory) some prescribed distance of the center of the Moon. Rinse and repeat with different distances, rinse and repeat again with different integration techniques.
The goal: For a given integration technique, find the best place to switch integration frames when using standard IEEE double precision numbers for numerical integration. Not surprisingly, switching to MCI immediately after leaving low Earth orbit yielded lousy results. Waiting to switch to MCI until the vehicle is extremely close to the Moon also yielded lousy results. Also not surprising, switching somewhere near the Hill sphere or Laplace sphere generally yielded the best results.
Somewhat surprisingly, it didn't seem to matter all that much which of the two (Hill sphere vs Laplace sphere) was used as a switching point (or some other similar value). Switching near the Laplace sphere gave marginally better results than switching near the Hill sphere for most techniques, but it was the other way around for a few techniques. The distinction is small, not quite how many angels can dance on the point of a pin small, but close to it. Just pick one. I generally pick the Laplace sphere, but that's a bit arbitrary. The space is rather flat in the vicinity of the Hill sphere or Laplace sphere.
You are using patched conics as opposed to numerically integrated trajectories, but the same concept applies. Just pick one, and then be consistent.