Standard quad VTOL plus rear pusher with tilt, how to setup

I want to bild a VTOL plane, quad VTOL plus one pusher motor, but I want to use the pusher motor for lift as well (the reason is I need about 12..13 kg MTOW (it is all around a starlink mini…), and I want to use dirt cheap 3115 motors, from Hobbywing (15 USD/piece); the problem is that they can work fine to about 9.. 9.5 kg. a switch to 12..13 kg MTOW over four motors involves totally different, much more expensive motors (from 80 USD and up). The pusher motor can generate about 4 kg of thrust (with some reserve).

The pusher motor when tilted down, would be located some 15..18 cm. behind the CG.

The question is, how to set up physically the other four VTOL motors (adjust them around the CG, taking into consideration the thrust of the fifth motor or leaving the fifth motor out of the equation,i.e. basically, compared to normal VTOL, should the 4 motors be moved forward to compensate for the fifth motor thrust lever). My hunch is that yes, the 4 motors should be nmoved forward.

Second, how to configure and to drive the fifth motor in the ardupilot. The tilt motor mechanism by the way would be slow moving screw type taking about 7 seconds to move 90deg.

I am not sure if it should be driven by Q parameters or by some lua.

Q_FRAME_TYPE & Q_FRAME_CLASS designate the number of motors, their rotation, and map the pitch and roll authority for each. The configuration you describe is not supported by any of the current frame classes/frame types and would require developing a custom frame class.

If you want to use those motors. it may be far less of a headache to do a coaxial thrust setup (Octoquad X/H configuration, and one fixed pusher motor)