Is it possible to make planes land on mobile air staging when it is moving?
No, it is not.
It requires the unit to stop moving. Using a separate unit for this (like we did with the mobile factories) does not work either because the landing procedure of the game does not take into account the idea that the landing platform can be moving. It will land where the platform was when the dock command was issued and then suddenly warp to where the landing platform actually is.
A work of art is never finished, merely abandoned