I'm not sure if any of these will help, but here are some observations about my history with Summon on a 2015 P85D.
When I had MCU1 in the car, using Summon from the app was a nonstarter. It would move a few feet and then cut out saying that I had covered up something on my phone. After upgrading to MCU2, Summon via the app worked without fail.
While I had problems with the app and MCU1, using the key fob worked every time- in the event you have not used this function before, it's a long hold on the middle of the fob, then a press on either end to indicate the direction. The same can be said for auto-park while in the car, which is just putting the car in Park, waiting a beat and double-tapping Park again before indicating the direction and exiting the car. I would then use the fob to get the car out of the garage.
Within a month of ownership I set the proximity tolerances to the maximum available, and it can now navigate to within a half-inch of obstructions in my garage.
If I use Summon to park, the car will return to that same spot when using Summon to pull out. If I manually pull in, pulling out via Summon will cause it to meander to the end of the driveway and block the sidewalk. I'm sure I can adjust the distance in the car but I don't find myself in that situation too often so I haven't bothered.
Never in the probably 800+ times that I have used Summon has it caused the car to impact anything. If you think you can get it to park itself in your garage, it would be interesting to see if it continued to refuse to move more than a foot the next time you used it.
I set Homelink to close the door after each Summon at home, but I think it only triggers about half the time, and only when I'm parking, not departing.