I'm tired and may be wrong, but I think that trick is for the rail docker, not the rail basic.
It does work on the rail basic too. I have my public USDs set up with an undock button (c-button v-rail) and this will undock ships attached.
Depending upon the orientation of your drone rack you could try changing the direction of the rail the drone is attached to to help move the drone out.
It also appears that you can link an activation module to the pick up point and disable it for launch, just add that to your launch sequence logic. I don't know if it is a bug or an intentional feature but the texture changes when you do and you cannot use them in the "off" state it would appear.
I have noticed a weird anomaly that may help. My station is aligned to galactic north and my mining drone carrier is docked on the same orientation. When you arrive in the sector you wish to mine, realign to galactic north again and launch the drones. Once they have completed their mission, make sure you realign the carrier to galactic north again before issuing the carrier recall command. I'm not saying it will be perfect, but they seem to be able to find their docking points far easier for some reason. It also helps if each drone has its own set of pickup rails as they are not all trying to get to the same point.
Finally, with mining drones. I have often been caught out with there not actually being any asteroids in the sector to mine. The number of times i have been thinking to myself..."but there is an asteroid THERE!" Another 50m and you are in another sector and suddenly they burst into life.
Hope all that helps?