Ok, watching the video again closely, in light of the more detailed info from your photo, it is clear that at 2:31 (going forward) and 3:51 (going backward) it is getting hung up on the ledge. The fact that it continues from this point when you try again is consistent with the theory that the car is willing to "push" harder to get started than to continue once moving. I don't know how much you're willing to do to try to address this, but the next thing I would try would be putting a 1-2' long piece of 1/4" plywood over that entry ledge (probably right up to the edge of the floor mat) to make a more gradual ramp. If that enables the car to pass without stopping then you know that some sort of ramp there (there are a variety of ways to do that "for real") will solve at least that part of things.
As for the stopping for obstacle avoidance, which it seems to do prior to stopping due to the ledge, it would be useful to see little video of what the proximity sensor displays on the dash are doing when this happens. I assume you've tried different spacing settings?
I might give a transition a try if I want to use this feature a lot, will see.
Regarding settings, the distance setting is for front / rear distance only, not side distance. Side distance is set to Normal or Tight in Advanced settings. At least that is my understanding of how the settings work.