Firstly, make sure the component lead lengths are not catching on the solder nozzle, if they are cut them shorter.
If you are cutting them could you not get them clinched at the same time then you can do what you want with the Assembly and nothing will fall out.
Check that the solder wave is set up correctly so the flow of the solder isn’t actually pushing the components out, if this is then check the angle you are hitting the wave at and change to 6.5 – 7 Degrees.
The four up panel make sure you have the leading and trailing edge are well supported so the panel does not get sucked down into the wave too much.
Bean bags certainly do work as long as the board is held tight enough in the fingers.