Hovering a plane using Pixhawk (ideally) in one position with GPS lock?

https://www.youtube.com/watch?v=wGL5I8esuwA

I am wondering if it is possible to do something like the linked video above with a Pixhawk or other similar flight controller. I know Ardupilot can do it, but the thing I'm having trouble finding is the capability to do this with a flying wing such as the TBS Caipirinha since it is a pusher and not a puller. I think it should be possible, as it has the capability to accelerate vertically, but I'm not sure where to find it or how precisely the location hold is. I want to avoid having to use more than one motor on the Caipirinha but multiple rotors is an option (2 is my limit) on other aircraft. I just want to use the Caipirinha as a testing platform. If needed I will use thrust vectoring(for rudder control) but I would prefer that the Pixhawk could automatically toggle it for the sake of the battery (so I'm not using it all the time). The problem with finding the answer to this is that I want to use one pusher motor instead of multiple puller motors. I haven't seen anyone do that yet but if it was possible I would like to know how and where I can find it. Suggestions are also greatly appreciated!

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The problem with a pusher wing is that there is then no airflow over the control surfaces when stationary so there is no control to hold the hover. The airflow may only have enough effect if the plane is climbing vertically with some speed thus not in a hover.

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