To my knowledge all the uncorking that hasn't taken eventually gets resolved. Tesla identified early that they need a good connection to make it work. Also, we know that the firmware has to be reinstalled after the changes in order to implement them. On some occasions the only reason the uncorking hasn't taken has been that the firmware didn't get installed or didn't take. One way to test this is to get Tesla to "push" the latest firmware back out to the car of someone that didn't take. Although unless you are really remote it is probably just easier to revisit the service center.
It might be that the API could report P1 before the firmware install and uncorking was complete, but I don't think the API could report P3 after a successful uncorking.
SC tech sometimes forgets to set Performance to 1. You don't really need to reinstall firmware, they just need to reboot gateway in order for changes to take an effect, I'm not sure why they are pushing new firmware, it does reinstall DU firmware but change seems to be there since version 28.
In all honesty, connection to a vehicle is not required, Tesla could do uncorking for everybody with over the air update.